Fare classes (not travel classes like Premium Economy, Business, Economy) are having fixed prices, so full-fare economy (which Y fare class is) will always cost and arm and a leg, no matter when (re-)booked. And yes, when there isn't Premium Economy available, you'll be downgraded to full fare Y (in fact, this might earn more miles, and for European feeder flights, the feeder for a long-haul Premium Economy was always booked in Y, which gave a neat mileage bonus)

I've had a case where I was downgraded to Y (from a cheap Premium Economy) due to the same reasons as yourself here, but took the gamble. Flight eventually was overbooked, and back-then SEN in Y is (almost) first to get upgraded, so it paid off with a free upgrade (operational) into Business class at the airport. But that's pure gambling, and I only did so because I had to be on that specific flight.

So, no matter when they downgrade you (as long it's 15+ days before the flight), unless you paid an expensive premium economy - or even business class fare - an advance downgrade to Y will rarely yield much if any cash, and that's not what you should be looking for.

Thus, just as in your case, it's best to negotiate with the airline and find alternative routings, where your desired (and paid-for) class of travel is available. They do have quite some flexibility in such cases, but prefer of course to rebook within their own company, or in the case of Lufthansa, without Lufthansa Group. But I know cases where they'd re-book someone from LH onto SQ Premium Economy, so that's not unheard of. But you need to do some research yourself, because they won't really look into all available options, and prefer to tell you "tough luck, here is your full refund" unless you actively come up with an alternative and don't like what they offered you.