The two halves are matched and balanced so it is critical they go back together on the same spline. There really shouldn't be any reason to split the two to replace the U-joints. You'll need a hefty vice (or press) to press the joints out, other than that it's not too bad an exercise.
You mention Spicer Half shafts, which is a common reference term, but OEM shafts are not Spicer, aftermarket ones can be. The aftermarket ones are sold as upgrades but quite frankly the OEM ones are good for 600HP, the Spicer units came into popularity when OEM UJ's were like $300 ea. so it was cheaper to replace the whole shaft and the Spicer shaft uses a Ford truck UJ.
The Spicer and OEM shafts take different size UJ's (Ford truck vs. Metric), so best to check. To confuse matters Hall did a funky workaround when OEM UJ's were real expensive, he sleeved the OEM shafts and used the undersize Spicer UJ's which have a habit of spinning the sleeves and reaming out the shaft.
OEM repro UJ's with zerks are available from the vendors and cheap now something like $45 ea. so pull the sleeves if you have them and go back to OEM UJ's.