That is a lot of new credit added the past four months. I would suggest giving it a break until your home loan. You don't have any utilization issues, so adding additional revolving lines isn't really going to help your scores if they're being hammered by constant new account penalties. I would just try to put some distance between your most recent applications, and would also suggest reconsidering fully paying off your loans prior to the mortgage application, as there are scoring penalties for having no open installment accounts that could potentially cost you many thousands of dollars on the home loan.
As for the two cards you mentioned, approvals in the mid-600s would be marginal, but combined with very aggressive recent credit-seeking, it would be highly improbable to be approved by Chase or Citi.
I would ixnay Chase for right now. I believe they have a 5/24 rule, so if they pull your Transunion, there is a possibility you'll be denied. Especially with so much of your loan history being so recent. I'll let the vets here chime in on that, tho.
The Chase 5/24 applies only to the number of credit and charge cards opened in the past 24 months. Inquiries and loan products have no bearing. If the three credit cards listed are the only ones the OP has been approved for in the past 24 months, they would be 3/24.
Just hoping to have a thicker profile and have another account reporting good behaviors.
Unfortunately scoring doesn't really benefit directly from quantity. 100 accounts all reporting paid on time doesn't help any more than 10 accounts all reporting paid on time. What a thicker profile helps with is padding for some key scoring metrics like average age of accounts by giving you a buffer when you later open new accounts, and to a lesser extent for some things like percentage of cards reporting a balance - there is a penalty at 50% or higher so with two cards reporting a balance you would see this penalty (which can be quite small or imperceptible; it really depends on the profile) whether you kept the 3 or added a 4th. The key things for a good score are payment history, low revolving utilization, and time. Adding new accounts may eventually help you later with buffers to keep the other factors in check, but in the shorter term adding additional new accounts would be harmful or at best make no difference. Adding time since your most recent new accounts, inquiries, and late payments is the best thing for improving your scores.
3 is plenty to rebuild your profile. Sit on those until you get a mortgage. Request CLI when you can without hard pulls only. Do so every 6 months. I have never seen a situation where a mortgage lender views 3 cards as insufficient.
Must garden until 2/1/2022 to hit my goal AAOA. 