I agree. All things being equal, I don't think the razor is the source of the problem. Both the EJ DE89 and the Merkur 34C are excellent razors and often recommended for beginners to DE shaving.It seems to me your blade angle is wrong if the blade is not cutting and you are getting razor burn. Also, you need multiple passes so that you get gradual reduction. By the time you complete 3 passes you should have a very close shave without cuts or razor burn. Don't buy a new razor because your technique is poor; the DE89 is very capable of giving you a close shave. Here is some good advice on blade angle; Blade Angle | Badger & Blade
That said, I have all three, and while I enjoy them I would have to give the nod to the Variant on the basis of better knurling on the handle. While it and the Progress give very similar shaves, the Variant is easier to hold when my fingers are slippery from shave soap/cream.
My two cents.