At risk of being terribly impudent (and when has that stopped me), Amy I don't believe you can do much, other than erect a greenhouse and/or sit on the melon and keep it warm.

Amy, I had some of the same problem this year. I did not have enough mulch to mulch an area as large as the vines grew, and with all the rain we had the outer ends of the vines became over grown with grass and weeds. Those melons did not sweeten up and ripen like the others. If I had it to do over I would take some roofing shingles or roofing felt(only because that is what I have on hand) and placed the melons on it to give an island for them to lay in the sun. I am not sure if this would have worked, but I would have tried it anyway. Next year I plan on having more mulch or planting them in the garden.

My melons are already gone and the bed near cleaned. I expect most of everything cleaned by the end of the week.

I grow my melons on black weedblock, but this cold wet year has still been a bad one for them. There are still some sitting out there after most of the rest left on the vine split, grown to full size but refusing to ripen, week after week.

About ready to pull them, because nobody wants melons in this cold weather, even if they did finally ripen.

Mine are on a trellis. My husband told me I should slip a sock over it. I wanted to see if this was the variety we grew 32 years ago. It must have been a good melon year then, they were the best melons we ever tasted. It was green fleshed, but not called a honey dew. They came from Johnny's and I think were just called pineapple melons.

DH keeps telling me its a learning year. We have put SO much money into soil and beds this year and yeilds don't justify it. He considers it physical therapy for me. Maybe the fall garden...

AMY, I agree with your husband. My garden never pays for itself in food, but I get tons of fun from it. Plus I enjoy giving the food away.

I planted kale and turnips today and will continue gathering organic matter through the winter. I may even plant some cover crop or food for the wildlife. Gardening for me is not just a summer time activity. Even my wife is getting more into gardening and that just tickles me pink.

It has been interesting this year. I like trying new things, growing something I haven't tried before. I like having produce that I know has no chemicals on it. I'm not much of a cook, canning is hard for me, I can't lift big pots any more. Some where along the line we will find a way to balance out what will work for us. DH likes having lettuce and fresh herbs. I will try this melon again next year. And I will try to start it earlier and use the black material to warm the soil. The cukes shaded out the water melon this year. I would like to grow some of those, too. I have learned a lot this year.

We normally have no issues with ripening melons in our zones. Either your melon is a long long season...or you got started late.
My neighbor ripened watermelons (though I must admit not till early September instead of normal July) this year. So yes...I guess weather did extend things a bit :(

Sandhill Preservation, where I got the seeds, says 85 days to maturity. It is listed only as Ananas. Some other places on line say as much as 110 DTM. It was planted in late May. It was the same day as the trombocino squash, which grew and florished in a nearby bed. I transplanted 2 cucumber plants in the melon bed about the same time, they produced more than we could use. The melon plant sat there, growing very slowly, through June and most of July. I noticed the first melon August 20, and it yellowed and fell off like it was never pollinated. They were planted in the southeast corner of the bed, trellis on the east side of the bed. The only thing I can figure is the cukes, on the west side of the bed, but growing up a trellis on the north edge of the bed. and some potted peppers on the east side of the bed produced too much shade for them in the cool summer. OR maybe the bed was too shallow and they were trying to put roots through the weed cloth in the bottom.

I have no idea how big they are supposed to get, if I remember, cantelope slip off the vine when ripe? Maybe I should put a sling under them just in case.

So you have the old-fashioned, open-pollinated Ananas melon? When I grew that one, the melons began to mature either the last week of July or the first week of August. I likely put them in the ground sometime after mid-May but no later than the first week in June. That was quite a few years back. In the summer heat with abundant sunlight pretty much from sunrise to sunset, they produced ripe melons about as quickly as Hale's Best Jumbo, taking around 80-90 days. In less sunlight and cooler temperatures, they could take significantly longer so you may have diagnosed your own issue. The cool summer weather probably didn't help.

I never weighed my Ananas but I remember the first one was abnormally big---maybe 6 lbs or so. Most of them were somewhere between 3-4 lbs.

There are some hybrid Anana melons, like San Juan from Johnny's Selected Seeds, that produce a couple of weeks earlier than the O-P ananas.

They will slip off the vine at full slip, but when I trellis the kinds of melons that slip from the vine when ripe I either put them in a sling (I use nylon knee high stockings to hold the melons) so they won't fall from high up on the trellis (it is 8' tall) and burst when they hit the ground, or I pick them at the half-slip stage. Harvesting at half-slip does not have an adverse effect on the flavor.

If your melons are only a couple of feet above the ground, they likely won't burst open when the slip off the vine, but insects like pill bugs and sow bugs (if they are abundant in your garden) will be on them chewing away at the rind as soon as they hit the ground. Today when harvesting cukes, I found a pill bug on a cucumber 6' above the ground chewing away on it.