I don't understand why the thin client would reject it in both methods, so ill just post some general steps i'd take that work for me fine with my kingston USB stick.
The easiest method that works for me is the reformat on whole device option which unlocks if you run the tool as administrator. This should automatically create a 2GB partition that is bootable and in my case i am good to go from there.
Method 2 would be the HP USB Storage Format tool, you want to use this with the bootable dos option and point it to a copy of MS-Dos 7.1 (My image extracted should work but its been many versions ago since i last tried this so the compression i applied to IO.SYS to reduce the size could have broken this route). You could replace the IO.SYS with one from a 98 boot floppy and see if it generates the generic DOS boot disk then. And if that works you can always put my original IO.SYS back to regain the Windows 3.1 support and smaller footprint.
Method 3 would use Easy2boot, this is very slow on the T5710 but if you use WinRAR on the .exe file to obtain the original .IMA file this works to and it should be enough to place the IMA file (I rename them to IMG) on the DOS folder of Easy2Boot. Keep in mind this might cause the drive letters to be different so don't accidentally overwrite your USB stick.
My tools are specifically designed for MS-Dos 7.1, so you will not get a working result with FreeDOS. You can however just copy my files on top of a MS-DOS 7.1 USB stick if you manage to create one. Let me know if any of these methods work for you or whats going wrong with them.
And another thing you could try is make a BIOS update USB stick (Theirs is based on FreeDOS so that should work great), mine runs the latest bios so if yours is older it could be a reason its failing.