You could try using the Multiscan, DblPal, DblNTSC, Euro72, Super 72 monitor drivers in Devs/Monitors or if not Storage/Monitors. You say the horizontal scan rate is 31/80. Although these drivers only go as high as just over 29, I have had some success in getting them to work with an old CRT with a min horizontal frequency of 31.
If no joy you could try and source an old CRT like the Microvitec/Amiga 1438 monitor. They work perfect with AGA Amiga's but they are hard to find. Have a look on eBay and Amibay.
Or if you are happy to go with the TV option, go for a SCART connector. It offers higher quality than the RF jack. You can find these on eBay or at Amigakit:
http://amigakit.leamancomputing.com/catalog/product_info.php?products_id=226