Matteo, you are not crazy but you must be determined. The distortion tells me something is amiss with the AGC system -- incorrect AGC voltage or bad interstage coupling caps putting B+ on the grids.
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As for T11, the easiest way is to watch eBay for the part to show up. You can certainly build a new coil, or perhaps adapt a new part that you find with Google, but that will be more work.
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Good luck, and keep us posted.
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Dave