Initial configurations of Vulcan will use the same Centaur upper stage as the Atlas V, with its existing RL-10 engines.
So it will not really offer any cost savings over the Russian RD-180. But more as an insurance policy in case the pressure against Russian engines does not ease up as you have said. The BE-4 co-development is more of the same...a second option.
Even if they spend a third to have it ready for the next flight there are substantial savings. However, most of those savings will be 'profit-margins' for the commercial business (not so much military since there is a cap)
I was under the impression that SpaceX is paid more for military launches, in the $90-120 million per launch vs $70 million for a commercial launch of the Falcon 9.
He is now firmly in the assured launched business with the Pentagon so he'll also be getting assured long term contracts just like ULA.
That he is, I think going forward at this point in time, he is slated to get about 33%-40% of the military business.
The reason I say that space is a passion for him is that when he made his big money after Paypal went public, he put in all the money that he got, about $200 million into SpaceX and Tesla. Unlike all other Silicon Valley billionaires who never even put money from one successful venture into the next. They rely on their new found credibility to get other people to put up money and put in only a token amount themselves. Musk in contrast not only put in everything he had into it, but at one stage in the early days when the Falcon 1 had one failure after another, he was on the verge of being so short on money (because the $200 million was all gone) that he and his then wife made plans to move back into her parent's basement and he begged/borrowed money to make payroll at Tesla and Space X. As you probably know, Google almost bought Tesla during that time.
But he was always taken seriously by people in the power structure by his sheer brilliance. Michael Griffin (who headed the Q branch of the C...I....A, the US Gov. seed capital investor for crazy and brilliant ideas) was one of his earliest backers as early as when Musk was trying to buy decommissioned Soviet ICBMs from the Russians, as his first launch vehicle, one of his mad ideas. Years later Michael Griffin became NASA's administrator.