It's in fact almost impossible to see how any more breechloaders could have been got, short of completely changing the US Army's entire procurement model or converting Springfield to breechloaders (both not good ideas for other reasons).Ripley's defenders point out that the Federal cavalry was wholly equipped with breech-loading carbines, which was itself a prodigious logistical feat.
As for the research questions:
I think you need a pre-war pattern of massive breechloader production to be able to produce enough breeechloaders for any significant issuance, and the problem with this is that it's totally out of step with what the US expects to be doing. The muzzle loading smoothbore rifle-musket is actually quite modern at the time, and the US expects to fight a war with no more than 90,000 men (15,000 regular army and 75,000 three-months men, the maximum allowed by law) of whom not all will bear long arms as several thousand will be cavalry and artillery. The US has lots of rifled long arms in store in 1859 (more than it really needs for the expected purposes) and even an 1858 war scare with Britain resulting in massive demand for "better" weapons probably wouldn't provoke the set up of manufacturing in time... especially since there's fairly good odds it'd be set up in Harpers Ferry anyway.
Berdan's infantry Sharps rifles cost the Union three times as many carbines as they represented, because Sharps only had the one plant and could run it to make carbines or rifles. So basically more long breechloader rifles translates to far fewer cavalry carbines, and the cavalry needs carbines.
Simpler to use combustible cartridges:
There might be some potential here, but I'd suspect the benefit would be quite minor. The trick is that a combustible single-piece cartridge is going to have the percussion cap on the back, and you'll be dropping it down the barrel (which is about four feet long as a rough guess) which means it'll strike cap-first and potentially fire (goodbye fingers); that means you'll want it to be at least two piece (contained paper and separate cap).
This then runs into the problem that the ball with a pre-expanded base (that doesn't need hammering down onto an expander at the base of the barrel) is itself a minor technological innovation.
Ultimately, the problem with musketry in the Civil War is just that people never really got any practice with loading properly. There are examples from throughout the war of people who'd never loaded their muskets before getting into combat, or at least never having fired them first, and even of thousands of people in one battle not noticing that their gun hadn't actually fired and so loading it a second time without firing the first ball.
The whole of 18th and 19th century warfare indicates that this is not hard; you just need to have practiced it a bit.
As for doing more to train soldiers in marksmanship, yes, absolutely. There is so much that could be done that I'm restraining myself as best I can, but the simple answer is that the British (who did obsessive marksmanship practice) found basically no reason you could not train the majority of ordinary line infantry armed with the Enfield rifle-musket to the level of range-estimation and marksmanship skill that Berdan's US Sharpshooters achieved; the only requirement is time, and a little ammunition to acclimatize the soldiers with firing their rifle.
The rest of the ammunition consumed in training is there for the "test" to confirm what they've learned.