The problems I referred to were aimed at those considering becoming resident in Spain, since as a resident you are obliged to re-register your car onto Spanish plates, with all the encumbent complications that go with that.
Jack, if your MoT runs out while you are abroad, your car will not be road legal - any more than it would be in the UK. You cannot get a valid MoT in Spain for a UK reg vehicle. Do NOT believe anyone who tells you otherwise.
In your case, I believe you have no option but to get a new MoT before leaving the UK. I'm not familiar with the procedure for retaxing online so cannot advise on that, but as long as the tax is paid on time (and you can prove it at a later date if necessary) you maybe needn't worry too much about actually having the disc with you, as Spanish (and French) police are unlikely to ever ask to see it. Re-entering the UK might be a concern though, without a valid disc displayed. Could someone send it on to you inSpain? The important thing, however, is to ensure your car is road legal in it's country of registration for the entire time you're abroad. If it is not, and you (God forbid) have to make an insurance claim, your insurance will automatically be null & void.
As for insurance, check with your insurer before you leave that you are covered for the length of your trip - there are usually restrictions, and cover is usually limited to third party only (minimal legal requirement).