IF you can afford it, put metal on it. Period.
Done deal, never have to deal with it again, and good for resale as well.
I can't believe your shingles are toast after only 11 years. They are probably 25 yr shingles too. Such a rip off.
If you re-shingle, you will have to strip what you have off, and take them to the landfill, and pay by weight. Shingles aren't light! And they don't degrade in a landfill. Leave them on there, strap right over top of them, and put on metal.
The question regarding keeping the house cooler in the winter, the answer is no. The reason it stays cooler in summer is because of the air space between the metal, and the old existing shingles. If the shingles don't get hot, the roof stays cooler, which in turn keeps the house somewhat cooler.
S.