heater core is a bitch to replace. i wouldn't do that unless i knew beyond any doubt that it had an actual problem.

this is what i'd do.

at any parts store or online, get a couple of heater hose splice connectors and clamps. i don't remember the size 5/8 or 3/4? dorman makes them for a couple of bucks each.

cut both heater hoses in a convenient place along the side of the engine. use a garden hose to backflush the heater core in both directions. expect a lot of crap at first. then observe flow. if ok, move on and flush the block and radiator.

maybe replace the t-stat with a high quality Stant Super-stat at 180 or 195, your choice. don't use a 160. be careful on t-stat bolts and try to avoid breaking them. reinstall bolts with RTV on the threads to prevent seize and leaks. do not overtorque.

look for the engine block drain plugs hiding behind the engine mounts on both sides. mine were hex head pipe plugs and there were VERY VERY tight and seized in . use lots of pb-blaster or other penetrating oil and let it soak. the plugs are hard to reach, and tend to round off, so do NOT use anything except a tight fitting socket or locking vise grips to prevent rounding. flush the block from the top of the manifold - either the t-stat hole or passenger side heater hose. the objective is to wash out the rust and heavy deposits that have settled into the bottom of the block.

when reinstalling drain plugs, use a thread lubricant like liquid teflon or RTV and do NOT overtighten. its a pipe plug, so just snug it and stop.

flush radiator if you want to try and save it. consider a flush product like Prestone radiator flush or similar. it might help heater core too. use clear water for all this activity and don't waste antifreeze. if you have hard water with calcium, you can flush with hard water, but drain it ALL out and avoid holding any hard water in the system as it will calcify out as a solid, which might be what caused your original problem.

after all flushes and chemicals are removed, drain the block again and refill with mix of distilled water/AF.

edit - i'm sure you already know this but i'll write it anyway. after the block is drained and you refill the radiator for the first time, the coolant has to make its way over into the block. il'll take about 3 gallons total, and its takes awhile for the coolant to fill up the lower radiator hose, water pump, and block... so give it time to perk over and when you do start the engine for the first time, immediately tend to refilling the radiator and keeping it full. MONITOR ENGINE TEMP and don't let it overheat. after that, the system is prone to air lock at the top of the manifold and heater core. some people use an elaborate air purge procedure, but I've always had success with parking with engine slightly uphilll and allowing it to run up to normal temp with radiator cap OFF. let it run for 15 minutes or so, refilling radiator until full, monitoring engine temp, heater on hot. this verifies engine temp, t-stat, coolant flow through heater core. verify all hoses get hot and NO LEAKS. finally - fill overflow tank to max, put on radiator cap, and drive it for several days. you might hear sloshing in heater core for 1-2 days but it will usually work itself out. refill overflow tank to max as needed. DONT open radiator cap when hot.