The TB20 can cross mountains perfectly well – see the last trip for example.
The issue is weather. Warm front wx tends to have tops of FL200-250 and a FL250 aircraft is essential then, otherwise your de-ice will be working overtime enroute and that is a bad way to fly. And cold fronts can go a lot higher, although generally one can work between the buildups visually. This is where the PA46 wins (at a substantial engine/cylinder cost) as well as the bigger stuff like a TBM.
Remember FL250 in unpressurised means wearing masks, in general. Cannulas get very marginal. I’ve been to FL210 and one had to breathe very deliberately.
The SR20 is far less capable than a TB20.
Getting turbo owners to post their top overhaul periods is a constant challenge 
But more practically, as the OP is looking for a post-2000 aircraft, there are very few TB21 GT for sale. They just don’t come up much. Look here, S/N 2000 onwards, and you get the idea. Part of the reason is that Socata were quoting 6 month lead times on the TB21 (in early 2002 when I was looking).
Like Bosco said, nothing a seller says about the condition or history can be relied on. You have to do your own prebuy, and checking the paperwork takes almost as long as checking the aircraft.
johnh wrote:
Not my experience in the SR20! Though maybe that’s precisely why it is NOT a serious touring aircraft (imo).
SR20 is very under powered for takeoffs/climbs even when compared to load of 160hp/180hp but it’s an economical cruiser with all gadgets (but hey, just like new DA40s it’s for schools and hooking people on SR22s/DA42s upgrades), the NA SR22 does just fine up to FL140, one may go for the turbo if they wish FL240
That’s the theory, in practice, I come across load of turbos in UK, pity all of them fly bellow 3kft all the time except for LeTouquet crossings when they may get to 6kft to get a descent glide range…
Even for use in Alps, there are far more limiting factors than just engine MAP, high elevation airports* in Europe are VFR only, don’t have good landing distances with rough surfaces and huge slope, plus the required extra signoff for mountain bush flying, the turbo may allow quick climbs but one has to remember Jodels D140 and Maules are the kings out there this is nowhere like the flat long pavement runways airports in CO/AZ with ILS on both ends where the turbo on IFR touring SEP shines vs same SEP with NA engine !
The ones IFR deep inside the valleys tend to be for local guys only…
Peter wrote:
I think a turbo is not a part of the engine but, like the exhaust, is a part of the airframe. So the airframe manufacturer is not restricted by the TCDS as to which turbo they use. This is quite an interesting topic
Lycoming even lists the P/N of the turbo charger of their page on the TIO-540-AB1AD engine, suggesting a specific engine model is tied to a specific turbo charger. Also, that page seems to say that the only user of that specific model is the Socata TB-21-TC. I’m quite interested in the answer to that discrepancy puzzle, too :)
It would seem a bit wasteful for Lycoming to develop a specific engine model just for the TB21, with a specific turbo charger, and then for Socata to slap a different turbo charger on it :\
Thank you everyone for the valuable inputs.
