No, proximity to Frankfurt does not make it better.
Budget projections have already been discussed here. I am not enough of a professional to assess this, but if your budget of 450k just for the house is a pretty hard limit (I am not talking about a buffer because it will get more expensive anyway). Then honestly, I don't know if it’s worth just "trimming" the existing design.
Just a few reference points. People like to calculate with 2,000/sqm here. Depending on the region, that's sometimes a bit too much or too little. Near Frankfurt rather too little. Some say the 2k are already outdated and it’s more like 2.2 or 2.5.
But we are still talking about a relatively simple building mass and no upscale fittings.
Architects like to calculate in enclosed space. You can also calculate that with 450 - 500 euros per m3 of enclosed space.
In addition, you have your extra costs for slope etc. I have no experience with that at all. But at that level with a long outside staircase, retaining walls, etc., 100k for earthworks and outdoor facilities can also be quickly spent. Do you have that on your radar in your calculation?