Meaning that what you describe - while still missing the needed DETAILS - is either not accurate (because you are holding back relevant data) or not accurate because you have misinterpreted the results of your experiments.
If the first absolute sector or LBA0 is accessible and writable, you can partition the disk, at least in 4 primary partitions. (good )
If the first few following sectors, namely LBA1-17 are as well accessible and writable, you can install grldr.mbr to the disk, but you will need a small amount of good sectors, let's say 1000 of them to create a volume to host grldr OR if a few more following sectors, namely LBA 1-63 or better 1-127 are accessible and writable you can install the WEE to the disk.
And the disk will become normally bootable (to grub4dos).
Then you have "holes" (i.e. bad areas, not everywhere, but in spots ) all over the rest of the disk.
Now if sector (example) LBA 238975 is "bad" and cannot be read or written properly, it is "bad", and it remains "bad" NO matter which filesystem you are applying to the volume created on the disk that comprehends that specific bad sector.
You are seemingly telling me that you attempted making a huge volume covering the whole extents of the disk and by formatting it as ExFAT the filesystem automagically marked those holes as "bad sectors" (and of course - but you failed to specify this, the available space in this volume is much smaller than what is should be given it's size)?
And that you cannot obtain the same (or similar result ) through a full format and running CHKDSK /R on a NTFS partition?
IF this is the case, and provided that your (unknown) disk is compatible, you may want to *try* this tool here:
on the disk, and hopefully obtain an unreliable, with a senselessly filled up $BadClus, but working NTFS filesystem.
But it is also possible that the volume cannot be actually properly formatted due to the default placement of the $MFT by the XP format tool, which depends on size of the volume and on it's extents.
The extents of the NTFS partition might be critical and in order to find the "right" placement/size of it some experiments will need to be carried as while there are a few tricks/possibilities to "move" the $MFT, WITHOUT an EXACT, DETAILED map of the disk, it is impossible to even give you valid practical suggestions.
Generically speaking, on a 512 bytes/sector device, the XP FORMAT tool will create a NTFS filesystem with 4096 bytes/sector clusters with the $MFT starting at cluster 786432 with a size proportional to the size of the volume, but there are also other files, like the $Boot record which is 16 sectors in size that have a fixed address at cluster 0 ( relative LBA0).
There is a trick that - within limits - allows to have the $MFT at a different location/having an initial reduced size, that may be useful in this case, see here:
but again, without specific data I cannot say if it may work in your case.
Otherwise - if you are really convinced that the exFAT is the way to go, you can have on it a XP inside an image (RAW or .vhd) that was already tested successfully by alacran (see previous posts) or experiment with the Windows 8 BOOTMGR (hints given before in this same thread) or - again as said - continue where the experiments with the XP Kansas city shuffle method were left, but you have to consider how all these are either very experimental or downright new/unexplored/undocumented approaches, in any case all of them rather complex (i.e. NOT of the do that 1,2,3 kind) and will need, besides some time and patience, to be first tested on some surely working hardware before being possible to hopefully replicate them to your half-botched disk/hardware.