Reddit mentions of Continental Tour Ride Urban Bicycle Tire (27x1 1/4)

Great find. I'd take the wheels off and take the tires off the rims and clean the rims using barkeeper's friend. It's better to do that without the tires on, and then rinse well and wipe dry. You can apply wax to the rims after they are cleaned if you'd like.

There's always a chance there's rust on the inside of the rim if you see some on the outside. I'd not obsess over cleaning out the inside of the rim, but if the rust is bad and flaking I'd maybe want to steel brush that then put the new rim strip in. Yes, you're on the right track with switching out the rim strips. If the rim strips are rubber they'll likely break apart from being old and dried out, so it's good to replace those along with a fresh tube and tire. There are quite a few options in the 27" size. Continental makes a nice touring tire that I think would go good with this as it's more durable than what this bike would have originally come with.

https://www.amazon.com/Continental-Tour-Ride-Urban-Bicycle/dp/B002XYTLMY/

Keep in mind that the hubs may need new grease, or they may be overly tight. You can feel the resistance when turning the axle. It's a worthwhile servicing, but it requires a number of tools including cone wrenches and possible a chain/vise whip to remove the rear cassette.

This is a great project bike and will be an outstanding ride once you take care of the immediate issues. Tires and maybe replacing cables and tuning seem like good first steps. If you do replace the cables and you're OK doing grease work you can take the opportunity to clean and re-grease the bearing cages for the fork when you have the cables removed. You may need wrenches for that.

>...am I better off getting a cheap used road bike to see if I like it...?

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Honestly, it sounds like you and I are coming from the exact same place. So I'm going to answer this with a conditional yes. That condition is this: I may be biased. I say that because that's what I did and I'm VERY happy with it. Now, I truly do prefer my 37 yo 10-speed over my hybrid any day of the week... but I pretty much only ride on paved roads. I currently ride on these tires but I used to ride on these, which worked well for local hardpack trails and nearby greenways. So it doesn't have to be all or nothing.

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I checked out the Rochester Criagslist (since you linked to it, I assume that's you area) for some older road bikes, and there are quite a few available, but many of them are $200+. Occasionally you can find one like this one for $20. That's cheap enough that you can get a new seat (the originals were like medieval torture devices), pedals (I like these), brake levers, cables, chain, etc. all for under ~$100. (Of course, I also would do my own servicing of the bottom bracket, which saves the cost of an LBS doing it.)

Then I'd give it two weeks' worth of riding to see how it feels. If you don't like it, then you're out $100 and you post the upgraded and improved bike back on Craigslist for $200-300 like most people seem to. Then turn those profits into upgrades for your hybrid.

If you decide to keep the hybrid, but are uncomfortable with drop bars, you may want to consider butterfly bars. If I hadn't made the move to a road bike, I would have done this with my hybrid just to have more hand position options.