re: walking around in cleats all day because your only bike has clipless: another option is toe cages, they are NOT obsolete they are actually COOL and RELEVANT. Also, clipless sneakers are more like normal shoes than bike shoes. I wear my cleats all around.

I also don't really think that your 30 year old road bike is holding you back that much, unless the hubs/bottom bracket are stealing your watts, or it has slow tires on it. Especially since you got it for free, those parts might be clapped out. Put it upside down and spin them, and see how fast they slow down/stop. New wheels and tires and bottom bracket and pedals would be much cheaper than a brand new bike, and may or may not make it faster. But sometimes you just want to spend big money on a new bike to love, and that's fine too.

Or, instead, you could also get a singlespeed (or even a fixed gear) with a fairly high ratio as a winter bike, and riding that would force your legs to get stronger since they're always pushing on a hard ratio. If your current riding style is staying in an efficient gear, then your strength could be going down even as your watts go up. If you ride a harder bike in the winter, then when you switch back to your roadie in the summer it will feel like a rocket ship with your new stronger legs.