The syringe may or may not be good depending how chunky the chunkulator in the formula is and how much you want to get into the tire. I've been fine using the tube that comes on the top of the Orange Seal bottle. Carrying the stem remover in the bag and taking out the valve is not onerous. They're now selling valve caps that have the remover built in. The Stan's Dart also has a remover built in. So does the top of a Slime bottle, for Schraeder.
It seems like you should be able to top up the sealant by stabbing a big needle right into your tire but I haven't been brave enough to try it :-D I recall a post where someone repaired the latex tube in their tubular tire that way.
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Genesis 49:16-17