Is it possible to host one TXT record for a domain on a different server, and leave all of the other DNS information intact on the first server?

I am running a business site on a computer with a managed hosting company. Everything is working fine, until I tried to establish DKIM verification for emails sent from the server. This required adding a TXT record to the DNS information. That TXT record contains an encryption key, so it's a bit over 400 characters long. I couldn't get DKIM working, then discovered that the online DKIM checkers don't retrieve that TXT record accurately. What they retrieve is three or four characters short of the real record, so the record appears invalid. The hosting company has verified this, suspects the problem is in their house, and is working on fixing the problem. Is there a way I can have that one TXT record for the business domain hosted on another server, for example Google's Public DNS? I'm not certain whether this could work. Thanks!

It depends on the exact details. In the cases where a CNAME is valid, you could add a CNAME which you could use to have your records exist in another zone hosted somewhere else.

# example.org zone (on bad ISP)
foo.example.org. IN CNAME foo.delegated.example.org.

delegated.example.org. IN NS goodisp-ns1.whatever

# delegated.example.org has been delegated to other ISP
foo.delegated.example.org. IN TXT "blah blah blah ..."

But a CNAME wouldn't be valid in all places.

For example you couldn't have it at the root of the zone.

Also, it may be possible that some software that checks the TXT record won't follow a CNAME.