I'd keep the original engine in it ONLY if I wanted to keep it looking absolutely original, for shows perhaps.
Otherwise, most would probably recommend bagging the original 350 & going with a 400 or larger engine. Would keep all the original parts, for possible future sale, with the car. Some will pay more for original numbers matching stuff.
Since you don't seem to want a lot of power, a decent mild pump gas 400 would probably work well for you. and I'd go with a good rebuilt Q-jet carb. You can either use a factory iron intake or an Edelbrock Performer intake. Obviously, the iron intake will look more factory correct, for your Bird.
You can go with a front timing cover, pulleys, and all the bolt-on items that came on your car. Or, if you buy a '70-up engine, you can switch over to the bolt-on stuff that matches those engines. It's always a great idea to get an engine that comes with as many original bolt-on items as possible. They're getting harder to find & more expensive. Some guys are selling small items for ridiculous prices nowadays, or at least trying to. I consider some of it price gouging. But, that's where we are today.
If you decide to rebuild the 350, you could easily up the performance, with a 4-barrel and bigger cam. Easy to make 300 or more HP, with a mild 350. But, it'll cost just as much, if not a bit more, to rebuild a 350 as building a 400. Pretty easy to make around 350 hp with a mild pump gas 400.
Your #17 heads are good heads to use as cores to make a set of high performance heads. But, having it done right, with good parts will cost probably $800-$1000. Or you can just have a simple valve job done & get by pretty cheap, if you just wanna build it for low rpm cruising.
As the power increases, so does the cost. So, it might be a good idea to decide just how much you are willing to spend on an engine. That might make some of your decisions for you.