We're in the same boat as you, and (as you know) not too far from you. We always had an oat cover on our hay, and it always did fine. We typically take the oats off for grain for the cattle. We used a binder and thresher up until 2004 (don't laugh), and it was always a struggle to bind as the green hay would be coming up through the oats. In more recent years we do the same, but combine the oats direct. But several years ago we started to notice the same thing as you: The oats seem to be doing better and better, and smother out the hay in some years. Usually not a concern as the hay will come back strong the next year. And we'll frost-seed into the hay stand the next year if really a concern, but of course frost-seeding alfalfa doesn't work too well due to autotoxicity. (We always do a heavy frost-seeding regardless, because our land is so rocky we'll do anything we can if it helps us avoid breaking it up for a few more years).
I think part of it may be due to our soil (finally) seeing decent nutrient levels, but also due to modern oat strains being more hardy and competitive.
Last year was the first year we varied from our norm. We cut and wrapped the oats as baleage before they started to head out to give the hay a little better chance of coming though. I don't think we'd make a regular practice of it, but with it being so dry last summer we wanted to give the hay all the help it could get, and also have the wrapped oats to supplement our hay in such a bad year. And the hay stand seemed to turn out very well.
The first thing I'd wonder about, however (and what we've been doing for the past few years - and find makes a big difference) is making sure you're not putting an N-heavy fertilizer on when you're doing the initial seeding. Depending on where/how we get our fertilizer (often we buy in bags because Agrico doesn't like delivering bulk loads as far as us) I'll mix about equal parts K-mag and 6-24-24 fertilizer. So the end result is moderate P, high K (which the alfalfa and trefoil really like), but quite low N. The oats really tone it back when they have that low N to start. So the oats are less aggressive and thick, and don't choke out the hay as much. Of course, you can't go too low on N, as you need it to get your grasses established as well. But that hasn't been much of a concern with us because our grasses are limited to timothy and brome. Timothy will frost-seed fairly well, so we often spread some on the next spring to help thicken if we're concerned. And brome seems to take over quite aggressively, and getting it established has never really been a concern.
Interestingly, since we've started doing the lower-N fertilizer at seeding, the oats are less stemmy and aggressive, but I haven't noticed any appreciable difference in yield when combining them. I will confess that we don't pay much attention to exact yield numbers however: We just take what we can and it all goes to the cattle. But I have a friend down South who grows a lot of cereal rye and he told me something similar: You don't want too much N, because it'll just grow thick, stemmy, and lodge, without any appreciable difference in yield. You want the grain just a little stressed. The way he put it, you want the grain to think it's coming on hard times, so it puts its energies into seed production and procreating, rather than just lots of top growth.