For the pros and cons of changing frames, the Steamroller isn't all that limited on whether you can fit tires appropriate to what you're doing, but it is a shorter and more aggressive geometry. It has a shorter wheelbase, shorter chainstays, and steeper head and seat tube angles, all of which contribute to a harsher and twitchier ride than something longer and more relaxed. If you were to put tires on it that are on the plush, supple side and choose the biggest width the frame can fit (which it sounds like you might have already done) and then dial in the pressure with some experimentation, you'll have found the approximate limit of comfort for the bike in terms of the shock absorption type aspects of the frame.
For setting up the chainline on something like a Straggler, there's not all that many 135mm fixed gear hubs to choose from. The Surly one puts the rear chainline at 53.5mm. For the front end you have a high-level decision to make in how much you care about running a modern crank with outboard bearings. If square taper is acceptable, life is much easier because then you can use the spindle length to tune the chainline. For many intents and purposes, what that means is you can take a track crank that uses a 103 or 107 symmetrical spindle to get 42.5 chainline and then add 20mm to the spindle to get to around 52.5 and still be working within extent square taper spindle lengths, of which 127 is around the biggest. (There are some bigger ones out there but then it becomes a question of quality because they mostly exist for low-end applications).
If you want external, your options depend a lot on what chainring size you want to run. Boost cranks (the easily obtainable contemporary options) put the chainline at 52mm, which is fine, but don't generally have rings available past 34t (there are exceptions or ways of creating exceptions by appropriating direct mount spiders from other cranks etc, but we go into the weeds of product recommendations there). The simple thing to do is use a 104/64 triple external crank and run the ring in the outer position, which will put it in about the right spot, and 104 is one of the sizes there's a wide range of tooth count options out there for. At this point this would typically mean using an older crank, although a few 104/64 outboard triples might still be available new.