I have three of these now, a Coke, a Pepsi and a 1675, all with a DG3804 movement which is ICHS for the 15710 but CHS for the 1675.The reason why is that Alex at nemboscorner over on the sister site at rwg always has these popping up for sale. For $200 I think these are a steal. With the 2836 they are a bit more pricey pushing $300 last time I looked but still good value and that movement is arguably better.
If you want a CHS you are looking at a DG3804 "CHS lite" which is a tricky movement as per our guru
KJ2020. I have that in one of my BP reps, the BP 126713 TT rootbeer. It is slighly misaligned at times, but that does not bother me. It is holding up so far. I wear it perhaps once a week when I wear earthtones. My TD Li did have to reject 6 (yes six) because of faulty movements. I would stick with a normal ICHS movement for these.
I don't think these come with a clone movement, either the "timebomb" which is a noob movement anyway, or the more recent true clones.
I don't think you can go wrong with any of these with any of the ICHS movements. ICHS does not bother me, i am not a frequent flyer which is where CHS comes in useful, and I actually like the quick date set of the ICHS.
To me these relatively cheap BP reps represent what the rep hobby is about. A great looking rep, only distinguishable from gen when close to the eye, and then still only when you know what you are looking at, with a cheapo movement that still tells time well enough, for a very reasonable price. I do like and admire the high end reps with their cloned movements, but when all is said and done with a service you end up spending close to a thousand bucks and with the odd add on like a dial from a different watch i.e the ARF dial for a Noob Daytona, a gen crystal, etc etc you easily shoot up north of $1k, or even close to or at $2k if you calculate getting an orphan watch etc. That gets you 10 of these!
They are addicting though, I just ordered a nice BP Bluesy from Alex to satisfy my inner wideboy!
YMMV of course