Hi Frostbite
Like you, I have my own private domain (also no website, just for email) hosted by one provider and use a completely separate ISP.
Whilst my email has normally been pretty reliable, I am in the middle of what appears to be the first significant email problem in 12 months at the moment so I won't mention any provider names here - although I may do so later if and when all is satisfactorily resolved.
The only thing that I would add to the good advice from other PPRuNers above is that you should remember that you can transfer your domain name from one host to another in exactly the same way as you can your custom with an ISP (try Googling 'transfer domain name' and you'll see what I mean).
AFAIK no company 'owns' your domain name, your host only maintains your registration of the domain name and rents you server space for it - so whatever you do in the short term willl not be irrevocable.
My advice is to try it and see.
Gadget 