With your budget the Lamda Athena hands down. This sucker is super easy on the skin yet removes whiskers like nobody’s business.
I would like to thank you James for this priceless information.
To the original poster. If your 34C is the latest milder version, most of the razors on the market will give you a closer shave. But we also don't know if this is your first razor. Have you used other DE razors before?
Fatip Grande or Piccolo, Fatip Open Comb Slant(FOCS), Mühle R41, Karve Christopher Bradley SBG, Blackland Blackbird, Wolfman WR2 0.95.Please let us know where you end up, OP. I purchased a 34C today and paired it with a feather blade hoping it would be more efficient than my King Gillette. Unfortunately, it was only slightly more aggressive/efficient. I’m looking for a razor that can mow through my whiskers with one pass (not that I’d settle with one pass). The KG and 34C simply don’t do it.