It will be getting a bit warm in S Morocco by June I think. Easy to search temperatures region by region on the web to get a good idea. If you buzz down to Morocco fast, at least if you find it too warm for enjoyment you can head north again and spend more time wherever feels more comfortable.
Regarding tyres, there are not actually too many really sandy areas (particularly in the mountains!) unless you go looking (and I wouldn't recommend it in the hot season solo) E07s should be fine.
I don't know what the Spanish sections of the TET are like, other than the mountainous north. Best place to ask for details is probably the TET forum. Looking at youtube clips of eastern european sections a lot looks not too technical, and possible on much bigger bikes than yours, but there are bound to be some suprises. There is no shame in taking a detour - when you're on your own you can't afford to take big risks.
Remember to take some time off the bike. You've got a big, ambitious plan, and it would be a shame to be burnt out and exhausted by the time your girlfriend joins you.
Have a great trip!
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