It bugs me a little when someone solicits feedback on this forum, and then doesn't follow up and explain how they used that feedback. So I will try to give periodic updates on my search. Here's how I'd rack and stack the recommendations thus far.
Tier 1 (will field test)
1. TL/TL3 – A buddy bags these, and the plan is to meet up and throw them today. Two downsides: Innova doesn't run them in Pro plastic, and current inventory is low across all plastics (but I assume that in normal times there are plenty of these discs floating around). However, I do see that there are some 158g-160g Tour Series TL3s available, so perhaps one of those could work as the 'understable TL' to give time to start beating in a heavier one.
2. Pipeline – PDGA approved specs are nearly identical to my Stags, and I have a heavy SP and light PL on order that should in theory give a fair amount of stability separation. Also, inventory is surprisingly high (but perhaps they just had a recent run and this isn't normal?). Downside: I was really hoping to switch to a more popular mold, so that I don't run into my current issue later on.
3. Sidewinder – I was really excited by the Sidewinder, but thus far no one has recommended them. I know the numbers imply the SW is a more flippy mold than others under consideration, but I've seen plenty of folks throw stable Sidewinders (especially Champ SWs). I'll still give them a throw since a buddy has some spares, but I think the TL or Pipeline are more likely to win the spot in my bag.
Tier 2 (will test if I can find some to borrow, or if Tier 1 doesn't work out)
1. Insanity – This disc went from completely off my radar to heavily under consideration. I like that it is widely available in both a flat/stable plastic (Cosmic Neutron) and domey/less stable plastic (Plasma). Three downsides: I don't know anyone that has one I can throw, it's faster than what I ideally would want for this slot, and my previous experience with gyro fairway drivers has been poor. But the number of people that have heavily touted this mold has piqued my interest.
2. Drift – Looks like it starts out less stable than I would prefer, but could beat in to being a Stag and Hatchet replacement rather than Getaway and Stag replacement. I'm intrigued, but not enough to buy one unless the discs above it don't work.
3. Essence – the closest disc to a Stag that is also molded by Lat64. But inventory on the Essence is barely better than the Stag, and I'm not sure if I can find an Essence that starts off stable enough to fill my pop-top Stag slot. Intriguing mold but probably only one I would throw if I can borrow a couple first.
4. Crave – I would need to feel the disc in hand before being willing to buy a couple. PDGA specs make it look like it will feel very Leopard-like and have an uncomfortably narrow rim.
Tier 3 (thanks for the rec, I looked into it further, but this doesn't appear to be what I want)
1. Eagle X/L – E-Xs are too stable for what I want unless I buy DX Eagles, and I don't really want to rely on base plastic fairway drivers. E-Ls just seem like a wild goose chase to find, so I'm not sure how that would make me any better off than just waiting around for a once-per-year Stag run.
2. Exodus – glad I crowd sourced info on the Exodus. This mold was high on my 'want to try list' and I was strongly considering ordering a couple. Thank you all for steering me clear of it!
3. Centurion – appears to be a Leopard variant, and I don't like Leopard rims.
4. Lift – Reminds me of an Escape, which is a road I've been down before. I want something slower and more workable than an Escape so I'm assuming the Lift wouldn't work out.
5. Teebird – Too stable
6. Vulture – See Teebird
7. Millenium discs in general (OLF, OLS, etc) – probably too boutique of a brand for my taste. I want something more available than a Stag.