First of all Parker semi-slant is not relatively mild. It is mild.“Try a slant razor” they say, so I started off with the relatively mild Parker semi-slant.
You don't need a slant for closer shaves. If you want to only do 1-2 passes and get BBS you need a razor with more exposure and more gap. It doesn't matter if it will be a slant, a solid bar or an open comb.
Stay away from the Merkur 37. The current batches have been made milder than the ones 10-15 years ago. They even changed the teeth on the guard. I'd also advise to stay away from the Fatip slant, as even with 3 passes and a very sharp blade I am far from BBS. With the Parker semi-slant I can get a BBS.
Razorock Superslant might work for you but you need L3 + or L3++. Even the solid bar will do the job. Be warned though. My L3+ has a gap of 2.00mm.