Can stolen or otherwise tainted coins be laundered through mining fees?
They can, and for sure they will.
Do chain analysis techniques consider the fee portion of block rewards as tainted funds?
In general, they should not, because the miner pool is, unless proven otherwise, protected by the good faith principle.
Demonstrating break of good faith requires demonstrating only the miner pool manager knew the transaction.
Once a miner pool manager bad faith is demonstrated, the first time they'll have a huge win, then regulation will be enacted, then if they do once again, government crackdown will come hard on them.
e.g. if known stolen funds are moved in a certain block, the fees the sender pays end up "polluting" the block reward. I want to know how much weight this taint actually gets when it comes to chain analysis.
None unless bad faith proven.
Would the largest exchanges accept these coins as deposits?
If so, then a thief could launder the funds by colluding with a miner. e.g. do a self transfer that pays 10% in fees; don't broadcast the tx, just pass it to the colluding miner who mines it and later returns a portion of the fees to the thief out of the block reward.
No, the higher the fee, the most solid suspicion for bad faith. Eventually blocks chain police would build enough evidence to demonstrate bad faith.
If not, then a thief could taint every block's reward by simply self transferring a minimal amount with sufficient fees for next block. Then none of the blocks rewards can be deposited in any heavily regulated exchange. I guess miners could censor those txs if the thief's UTXOs are well known, but it's still an attack vector I guess.
No, they don't even need to censor it, if tainted fees are low, reward gets a very low taint, because most fees are legit.
What I can now unsee is a future where, long after inside countries anti mining laundry regulation has been enacted, nations hack each other's reserves and use their own mining rigs to launder coins stolen to the enemy, in blocks the enemy is forced to accept because multipolar global nation state consensus. Until a straw breaks the camel's back. I think you have discovered a casus beli for WWIII.