Sometimes i don't know how to advise, but if i can then i will go into points then you think about it and decide later.
1. "I shot wildlife at most, not so much birds in flight", this line giving me a sign of long lens, so i don't think you will shoot wider more than longer, for example, with 70-200 i am sure you will keep using 200 a lot and even that will be short many times unless you can get closer but this is another issue to get closer.
2. "one of my local shops have 20% off on Canon 70-200/4L IS USM", so just because of that deal now you think about it, what if there is no deal? and did you think about this first place or before?
3. Canon EF 200/2,8 L II USM is a prime lens and very sharp, maybe sharper than all other lenses you mentioned, and you can use it with TCs, so you can get 280 f4 or 400 f5.6 if we assume you use a full frame, and still you can have sharp or acceptable results more than zoom, in wildlife/birds even if you have a longer teles you may add TC, so i assume with those shorter lenses you definitely will gonna use TC sooner or later, so in this case primes to me is the winner.
4. "I loved 2.8 when I owned the Sigma 120-300", believe me, when you go with f2.8 enough time, you will have difficult time to get used with f4 even it will do the job, so think carefully what you need to sacrifice, i wish if you can win that lottery then you will buy either 70-200 2.8IS or even 200 f2L IS and never look back, but if you really win the lottery and want a lens for wildlife/birds, then nothing less than 500-800 lenses.
So why not buy Sigma 120-300 again? there is a sport version which is better, what about Sigma 150-600 sports version then over your Tammy 150-600, and what is your Tammy lacks of that you need another lens for wildlife/birds?
If it was me, then i will look at f2.8 lenses options first, so the last 2 you posted, but let's give only cons of each lens then you think more wisely:
1. Canon 70-200 f4L IS, it is f4 and heavy lens than 200 f2.8, not sure how that lens compared to the Tamron one
2. Tamron 70-200, AF and sharpness is slightly less than Canon versions even it is f2.8, so i know if i have this Tammy i still will dream about Canon or even Sigma
3. EF 200 2.8II is a prime lens, means it is limited for distances, so you must be the zoom here, many prefer zooms even less quality just for FL range ability.