CreditScholar is on the money. Especially since work frequently puts you in Hilton, I'd focus on Hilton for both work and personal travel and aim for the highest elite status tier you can get in order to maximize your point accumulation rate.
It's a different consideration for those who travel infrequently and don't have a lot of actual hotel-related spending, because the tier bonuses don't earn you extra points from other spending, only from Hilton spending. But since you actually will be spending significantly on hotels, it makes sense to maximize all those reimbursable dollars for as many points as possible.
Citi HHonors Reserve is a great place to start since it will get you gold status right out of the gate.
But I would also apply for the no-fee, non-Surpass version of the Hilton Amex in January. The rewards on it aren't as nice as the Citi card, but it would get you the benefit of backdating and the AXON award redemptions exclusive to Amex that can make your Hilton points stretch further than they would with the Citi card alone.
As for the Ritz-Carlton and Hyatt cards, those are already hotel transfer partners for the CSP you are already paying an annual fee on. So I'd focus on the Hilton card but use the CSP and Freedom in categories where it makes sense (Freedom 5%, dining, travel purchases) to accumulate UltimateRewards points you can use at either chain.
The Amex Platinum AF *can* pay for itself, but it really depends on how much you are able to make use of all their benefits. The lounge access, for example, isn't that valuable unless you actually have time to lounge. Nowadays, it seems that employers and airlines both book travel itineraries and work agendas so tightly that I'd never have more than 10 or 15 minutes to sit in a lounge. I used to want a platinum, but I did the math and determined that right now the benefit isn't there for me.
The Citi HHonors Reserve has no foreign transaction fee, and the CSP gets you 2x points on travel expenses, so I don't see any need for you to add the Venture card.
Bottom line: focus on the HHonors points, make UR points a second priority. App the Citi HHonors Reserve and the no-fee HHonors Amex (ideally this one in January).
If you want to add something else, beyond that I'd look into what airline I fly most frequently for work travel and get the best miles card available for that airline.
Have you considered the AMEX Hilton card? There is no annual fee.