I’m sorry for the inconvenience…
The exact relation between OTF and TTF is still mystery for me. As far as I know OTF should just encapsulate TTF with slightly different header. I use mainly High-Logic Font Creator and it offers export to “TTF/OTF” as a single (!) format but it always adds “.otf” extension. Now I tried to convert the OTF file through Convertio and the resulting TTF is exactly the same file. I guess OTF can (but does not have to) be the same as TTF. In this case renaming to TTF work just fine. 
Here’s my (hopefully) final version:
Some (about five of them) diacritical marks are still placed at half-pixel position (e.g. Abreve) but all other versions I created looked worse to me so I kept them that way. The rest should be fixed.