I grow Table Ace. The stem doesn't turn brown but remains a dark green. The squash develops a 2-3" dia yellow spot underneath when its ripe. I grow quite a bit of winter squash, and find that just brushing off the dirt, instead of washing them, is the best way to preserve them for any length of time. They all have a protective layer of natural wax, and Table Ace particularly so. Table ace is one of the most productive squash (fruit per sq yard) I've ever grown. They'll turn completely orange during storage. It's a good 'un. Here is a link that might be useful: acorn squash factoids

The first thing that comes to mind is lack of pollination. You may need to hand pollinate the females flowers. There are a number of threads on hand pollinating you might want to do a search here or look in the FAQ. Another thing that may be causing it is if the plant is stressed (too much rain, too little rain, too little nutrients.) The plant will abort the fruit if it can't support it.

There are round eggplants, Thai variety I believe. I think they are usually striped white and green. You may have planted hybridized seeds. I got some hybrid squash seeds in the packet of yellow crook neck seeds I purchased this year. After the plants began to produce, I found that a couple of them aren't true yellow crook neck--they are crossed with another type of squash. They are edible, just not what I had in mind when I planted. Lorna

A couple possibilities come to mind that may or may not be helpful. The first might sound silly, but are you sure the female flowers are getting pollinated? We have few pollinators in our area, and I've been hand pollinating this year. The success rate has gone through the roof, with even an uptick in zucchini setting on. Some would see that as insanity, of course :) And just in case you aren't already aware, Butternut (C. moschata) and Acorn (C. pepo) generally can't pollinate each other. It's also possible the vines don't think they're established/mature enough to bear fruit yet. Another possibility could be, as you noted, a watering or nutrient problem. Blossom end rot (BER) affects more than tomatoes, unfortunately. My understanding is that BER is caused by a calcium deficiency within the fruit, the root cause of which is uneven soil moisture. If the soil alternates between too dry one day and too wet the next, it might cause a problem with calcium uptake. Along those lines, but perhaps not as common, is the possibility that the soil pH may be so high as to interfere with the availability of calcium. I've only read a bit about it, though, and don't know if it's yet another urban legend. Anyway, those are my thoughts. With a little luck, one of the squash experts can chime in with more information. I sure do envy your hoop house. Good luck! Here is a link that might be useful: Hand pollination of Squash