I'd certainly be doing this on the saw.
I'd only use a router if saw wasn't available. Way too much dust and noise for my liking.
Swapping the cuts around though (1 for 2 and 2 for 1) and having rebate/waste against sub fence which is sitting above waste height.
No side pressure needed but an additional side batten/guide on the saw bed will keep things lined up nicely on both passes.
Cheers Andy
Quite like your suggestion Andy, but not sure why you would alter the sequence of cuts. I would assume that making the 34mm cut first when there was more stock around and then do the 14mm cut where the chances of any binding would be much less would be better.
Richard