Sounds like a One Act competition. We either coil them and use tie line, or if we have a lot of cords to handle, we use an extension cord reel such as this. Reel the first cord on, then plug the second cord into the first, and reel it in until you fill it up, then move onto a second one if needed.
I have this same electric corded mower and I freaking love it! I've had it for 4 years now and it works perfectly.
I DO NOT miss using a smelly gas mower. I always hated having to go fill up the little gas can and smell up the trunk of my car, then when you're using the mower it stinks, and when you're done your garage will smell like gas for a couple days. Keep this in mind OP, you're currently storing the mower in your basement? I would absolutely hate to have to lug a gas mower down some steps and have it stink up my basement.
As far as the cord, it's really not that big of a deal if you just plan right and get used to it. Make sure you at least pick up one of these to roll/unroll. Just get into a pattern of rolling out the cord on the ground along the side of the yard with the plug, and mow from that side of the yard to the other, keeping the cord on the side you've already cut. (I cut a bit weird though, I don't turn around at the end of each row and always push forward, I stay facing the same direction and just walk forwards and backwards, scooting the mower over a bit before going in the other direction. This makes cord management way easier IMO.) I'd rather deal with a cord all day long than a gas can. And I also DON'T miss going to start that gas mower for the first time of the season and... damnit... fucker won't start... pull... pull... pull... take a break... pull... pull... cuss... pull... fiddle with it... pull 20 more times... IT STARTED! ^(((pray it doesn't stall on some tall grass cuz you may never get it started again!!)))
I love how quiet the electric mower is, and as many times as I want I'll let go of the safety bar to let it turn off so I can pick something up that's in the way, and it starts right back up immediately at the touch of a button. Sooooooo freaking nice.
One thing to think about if you're considering a reel mower. I tried one too before I got the electric one. It didn't work out. If you have ANY amount of little twigs (even tiny ones) or pecans or large acorns, you're going to get about 2 feet and it will get hung up and you'll have to fiddle with it in order to get another 2 feet before it happens again. If you grass is clear of all that, then yes, they are a pleasure to use. I wish I could myself, but it's just impossible with the constant falling of bits from huge branches covering most of my lawn.
Once I started using one of these, I never looked back: