I will second what Truckinbutch said about the ease of steam injection. It is the simplest and easiest way to skin the cat. The main difference is that if you tell people you are running cleared mash in your boiler and the thicker stuff in your thumper they will nod and approve, and if you tell them you have a steam injection distillation system they will get uptight about the number and type of pressure release mechanisms you have on the steam boiler. I speak from experience. They are the same thing, but... All joking aside, make sure you can never build more than a negligible amount of pressure in any distillation related vessel, and make sure that if you do so accidentally that it can be vented safely. Same thing goes for negative pressure. There are plenty of internet pictures of kegs and other vessels crumpled from the effects of holding a vacuum as they cool. I am sure you know all that.
As for the benefits of copper over CSST in terms of heat transfer, I have real data on it, and it doesn't jibe with conventional wisdom. Conventional wisdom accurately states that copper has better thermal transfer characteristics than stainless. That is true, but it leaves out important information. Corrugated stainless is much thinner walled and has a much greater surface area than a similar specification of non-corrugated copper. For $1.26 per foot on Ebay, 3/8" CSST has a much better performance "IRL", as the kids say, than copper of a similar cross section, both in terms of doing the job and cost. In other words, the added surface area of the corrugations plus the thinner walls to transfer heat through more than compensate for copper's clearly superior thermal transfer numbers.
They say a picture is worth a thousand words, so here is a picture that illustrates the thermal transfer characteristics of a 25 foot long 3/8" CSST wort chiller coil chilling a 10 gallon pot of boiling water versus a 25 foot long 3/8" copper tubing wort chiller versus a 25 foot counterflow chiller of a similar diameter versus a plate chiller doing the same thing. It is an inverse (but equal) example to your mash/still heating problem. The CSST is superior to all but the plate chiller, which is a seriously more expensive option and only works on beer wort or other liquid without much solids content. You can stick a CSST wort chiller/heater in your pot of mushy mash and get it cooled/heated much more efficiently than a copper coil.
In all, I would recommend you avoid the whole issue and direct inject your still and use the CSST in condensers of various types for distilling and HERMS units of various types for brewing. You mention direct injection as part of your process. Why is it unacceptable to use that for the whole thing? It will always be more efficient than indirect steam heating. With direct injection ALL of the heat goes into the pot.