Those Williamite soldiers would just have seen their king die and their army defeated and as you pointed out were themselves disproportionately second rate. Are you really assuming none of them will desert or outright surrender? And of course to what extent are those soldiers Dutch or other foreigners in Dutch pay and thus as say vulnerable to just abandoning Ireland altogether?
I don't doubt Mary will have troops available... but a whole second, front line army? That would take time and during that time James will have recruits flooding in from across Ireland.
OK I think your vastly overestimating the situation in the British isles at this point. William III is dead. His army defeated, and demoralized at having just seen their leader killed.
Obviously the Williamite forces would be in serious disarray, that's inevitable after a battle and twice as inevitable when the General also dies. And you're obviously correct in that the Dutch and Danish* troops (who are the most disciplined and best troops in the army) will be withdrawn rapidly. But William had 20,000 British and Ulster troops and while a large portion are either going to die on the field or desert we can assume that at the minimum 10,000 will be alive and in formed units within a few weeks. Add that 10,000 to the second line troops elsewhere in Ireland and you have a force that's only a bit smaller than the Jacobite army (26,000 minus at least 20% battle casualties on the Boyne). Now those troops are scattered all over Ulster and with shaky morale and relatively poor experience. But Jacobite army was also mostly made up of raw peasant levies and was much less well equipped than the Williamites. So while the Jacobites will have an advantage in the aftermath it won't be overwhelming and they definitely won't be able to quickly secure Ireland.
The Dutch states-general will take temporary charge of the Republic and no doubt rather quickly recall their forces from the British isles and be put on the battlefields of Europe. And the Danish mercenaries will also be up for grabs with their employer dead. Also your forgetting a key player in all this: France. OTL Louis XIV was reluctant to send that many troops to Ireland, but here things will be different. With veteran French troops backing them up, I think the Jacobites could rather easily overtake the remaining Williamite garrisons in Ireland. And a victory in Ireland could easily lead to further risings in Scotland as well, which could be backed up by Franco-Irish troops. Really killing off William III would NOT simplify matters at all, but instead create political chaos in both Britain and the Netherlands.
You are entirely correct that the death of William III would not be GOOD news but I do think it would simplify things. Whereas in OTL William was divided between securing the British throne, defending the Netherlands and helping the Austrians as part of the Grand Alliance here everyone would be more focused. The Dutch would pull out their troops and focus on defending their homeland from Louis XIV. As in OTL they would find it difficult but Louis would have his attention divided between them and Austria. Mary II in contrast while firmly committed to the war and the Grand Alliance is naturally going to focus on securing the British Isles and only after that is going to send troops to Europe. Austria is in trouble, with Mary II focused on Ireland and the more "selfish" States General prioritising the Netherlands Leopold I is going to get a lot less help.
As for French aid to the Jacobites a victory on the Boyne is going to see it stepped up. But there is a clear upper limit to what Louis XIV can or will send, remember Ireland is a tertiary theatre, there is the Central German Front, the Dutch Front, the North Italian Front, the Catalonian Front plus the Colonial Conflict in North America and the Caribbean. Ireland is a great way of keeping Britain distracted but if Louis has to choose between Ireland and Strasbourg it's a no brainer. So in the aftermath of a (highly unlikely considering the disparity of the two forces) Jacobite victory on the Boyne we are going to see London send troops, supplies and money in order to rebuild its Army in Ireland and reverse the setback. James II is going to get even more Irish peasant signing up plus French muskets and power to equip them and maybe even some French soldiers to train them. But in the long run (and remember this is year one of the Nine Years War) Britain will pour in more troops and money than James and Louis can match.
*who are in the pay of the Netherlands and are effectively Dutch as far as this scenario is concerned.