This sounds like steam to hydronic conversion at some point in it's history?
There's no restoring the flow capacity of corroded up iron- it's done. Ideally you could pull the old pipe and be rid of it to use the same chases & holes to snake in some PEX, but there are few cases where that's easy to do. If this is a DIY weekender project, wait until the heating season is over- this could take some time. Oxygen barrier PEX will be nicer to any remaining iron in the system (like iron pumps & boilers) than the cheapest stuff, and will be far easier/cheaper/quicker to retrofit through walls & plumbing chases than sweat copper, etc. If you've been running the system at 180F or higher you'll have to back it off a bit to use PEX (but with the higher flow it'll likely still deliver the heat at 150-160F that it was at a 180F trickle.) If you can, insulate any of the new pipe as you go with 3/4"-wall closed cell pipe insulation wherever it goes through unconditioned or semi-conditioned space like unfinished basements/crawlspaces/attics. (Don't us the cheapo 3/8" wall stuff available at box stores- order it online if you can't find it at your local supply houses. Grainger carries some.)