Usually investable assets help you get better rewards on cards in a few programs like BofA or Fidelity, but having those matter in order to get credit requires some kind of relationship with a banker who manages your assets and their ability to influence credit decisions. US Bank seems to give it's bankers the ability to influence credit decisions for their cards, not sure of others.
I will say that most people with good credit/cards in the US have it done it without any investable assets influence. There's no easy way to game the system in a way because it requires time and on time payment history and a building up from starter cards to better ones in most cases.
Do you have any credit history in the US at all or just starting from scratch? Getting denied for too short of a history makes me think it's brand new file and if that's the case then you've started it right, get any cards you can to start building on time payment history. Your score will grow over time (pretty quickly if you don't miss payments) and you will be able to get any card you want within a year or two.
I never had any relationship with Citigroup before except for 2 credit cards - DC ($12,000) and CC ($11,600).
Then, I put $75,000 into their Citibank Priority checking, got my $1,000 bonus, then put the $76,000 into a 1 year CD where it is now.
Then, I applied for the R+ card. $7,500 limit. So, having $76k with Citibank didn't help me with citi cards as far as I can tell.
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@johnl8003 While you might not be looking at Chase, I'll add that my experience with them is yes, moving over assets appears to have had a substantial positive impact. After funding a Self-Directed account and upgrading to Sapphire Checking, the flood gates seemed to open for CLI's, as can be referenced by my experiences here and subsequently here. I think this helped my case for overall exposure, but might not necessarily help with easing initial approval criteria (such as applying over 5/24).
Welcome to My FICO Forums, @johnl8003. 
You bring up a topic that is often debated on My FICO and I believe the answer is "it depends." In your case, I think the influence of moving assets would be minor if anything. Money talks, but to really open doors it would probably need to be much higher than your mid six-figures, or at least be accompanied by a similarly large documentable income.
Whether the credit and banking departments talk to each other depends on the financial institution. Bank of America is known to heavily favor applicants for their Premium Rewards cards who have deposit accounts and Preferred Rewards status, for example. But I'm not sure that is enough to out-weigh a lack of credit profile depth. Same with the other major lenders.
I would suggest continuing to build history with your Capital One cards and over time, try to add another bank card. CITI, as you've seen, is known to be a little more picky on their underwriting. Discover is often an easier approval. AMEX might approve a card with a thin profile, especially if you have higher income. (I'm not sure if it helps but they have an online money market where you could park some funds at a decent HYSA rate.) AMEX approvals are often easiest on their cobranded cards (Hilton, Marriott, Delta) followed by their charge cards and then lastly their core cards (BCP, BCE, ED, EDP, CM). If your ex-pat status is due to parent's military/goverment service, you might be eligible for Navy FCU and they have more lenient underwriting with thin profiles.
Your idea about HSBC might be a good path, but I'm not personally familiar.
