You are much more up on all this than I, would you mind sharing specifics?
In Vegas we have an issue right now where most of our pairings are a 10 or 11pm showtime to go to East, then day sleep and head west. It takes up three days and only plays ten hours.
I know you now the basics of these, but I'll spell it all out as there are a bunch of people who probably don't.
Soft time (credit without block) pay is designed to force efficiencies, not as a way to be a money maker. The best you can do (unaugmented), depending on a bunch of part 117 things, is 9 hours a day. There is no soft time pay that will get you anywhere close to that, outside of irregular op/reschedule stuff. The most efficient trips (more money/more time off at home) will be crammed with lots of flying, not soft pay rigs/work rules. That said, depending on the nature of the flying, or the sophistication of the people building the schedules, it may not be possible to do efficient trips, which means pay rigs and soft time rules are necessary to ensure the MMMTO thing. The combination of rules work together to give a pilot the greater of the different things, to maximize their pay over the course of a trip.
Trip rig: get paid X hours per every X hours you are away from domicile.
The industry norm is 1:3.5. This means you divide your total time away from base by 3.5 and that's the rig. Efficient groupings almost always don't pay any trip rig. It is designed for sitting around a bunch during your trip. Even if you have a bunch of flying on some days, but none (or very little) on other days, because it is applied across the entire trip, it tends to not pay out very often. It does tend to pay for trips that start early on day 1, and end late on the last day, because you are often sitting around a bunch somewhere in there to switch from an AM to a PM type of schedule. In your Vegas example, where you leave late on day 1 (say 10pm) and get home early on day 3 (say 2am), your TAFB is relatively low compared to the flying you are doing, so it won't help a bunch. With those hours you are getting a TAFB of 28 divided by 3.5 for a trip rig of 8 hours, which is probably well short of the block of two transcon legs.
It's it would be a heavy lift to get something better than the 1:3.5 that properties have as pretty much nobody has more than that.
Duty rig: get paid X hours per every X hours you are on duty.
This varies greatly from company to company and at some places it varies depending on how long your duty period is. Because it only pays for a duty period, it doesn't help you at all on days when you don't fly, or you only fly a few legs with no length sits. The duty rig is often overridden by a duty period min anyways. With your vegas example, because you are only flying 1 leg each duty period, the period itself is only a bit longer (figure 1 hour for a show time and 15 minutes for a debrief?) than the block time, and any ration won't pay out greater the block at all.
Min Duty Day: This means that any day you have duty in, pays a certain amount. This (generally) isn't averaged over the entire trip, so if you fly a lot on day 1 and day 3, but only a little bit on day 2 and trigger the min duty day, it is added in with your credit from days 1 and 3. The problem is if you do nothing on day 2, because you weren't on duty, it doesn't trigger at all. Depending on what your number is, and the actual language in the contract, this may help you in your Vegas example. Let's say it's 5 hours (which is right in the middle of the industry). You have duty on all 3 days so in an ideal world, this would pay 15 hours, which is much better than the 10 hours. However, some contracts have stipulations that you need more than X hours of duty on a given day in order for that day to count (so the 10pm departure on day 1, and the 2am arrival on day 3 may not even make those days count), or the credit is only applied to the day in which the duty period starts, so you'd get one for Day 1, and one for Day 2, but nothing for day 3. These are relatively common carve outs.
Min Day and Average Min Day: To get around the problem of having a day with no flying, and only having it count towards TAFB, most contracts have a min daily guarantee. That means for every calendar day you are on your trip, you'll get X hours of credit. The industry is between 5 and 5:15 on this one. Some contracts have carve outs as well, so trips that begin after 10pm or so on day one or get done before 4am or so on the last day, don't count towards the total number of days. The other issue is that almost everybody has an AVERAGE min day, which means the entire thing is averaged over the trip, and tends to get wiped out by higher block days. So if you have a 5 hour Average Min Day, and fly seven hours on day 1, four hours on day 2, and four hours on day 3, your AMD won't pay anything. A "true" min day, would pay 5 hours each day, so in this case, days 2 and 3 would benefit from an additional hour of pay, and you'd get 17 hours for the trip. In that example you'd actually be covered by a min duty day as well, which is more common, so, assuming the min duty day was 5 hours, you'd get 17 total.
I'm currently on a 4 day trip, that has eleven hours on day 1, no flying on day 2 (hello hotel jail!), and then 8 hours that spans days 3 and 4. The total TAFB is 71 hours.
-If I was only paid based on block, it would be a four day worth 19:00.
-We don't have a duty rig for this kind of flying, so it's a moot point. Even if we did, both duty periods are only 90 minutes (60 minute report/30 minute release due to customs) longer than the actual block, so a 1:2 or even a 60% on duty (which is pretty much the longest in the industry), wouldn't be very helpful.
-We don't have a min duty day for this kind of flying. If we did have one, at say 5 hours, it would pay 5 on the first day (but I'm already blocking 11, so that doesn't matter), and nothing on day 2. Day 3 would pay 5 hours. We accrue credit on the day a leg starts in, so that 5 would be wiped out by the 8 hours of flight time. Some contracts would pay the additional 5 hours for the last day (because it has duty in it), but some wouldn't because duty periods that occur in multiple days are only credited on the first day. So with a min duty day, the trip would credit 19, or 24, depending on contractual rules, but most likely 19.
-Trip rig would pay about 20:17, based on the 71 hours of time away from base. This is greater than the block time of 19 hours.
-An average 5 hour min day would pay 20 hours (4 days X 5 hours).
-A true min day would pay 29 hours (11 of block on day 1, 5 hours of credit on day 2, 8 hours of block on day 3, and 5 hours of credit on day 4).
So depending on the rules in place, this trip would pay anywhere from 19 to 29 hours. In most scenarios, a true min day (that is sufficiently high enough) will pay the most, however, because of that, almost nobody has it. With that in mind, the most efficient method of boosting soft time is a combination of average min day, and trip rig. This protects you against the fly a bunch on day 1 and 3, but do nothing on day 2, and from the start super late on day 1 and end super early on day 3 (which minimizes TAFB).
