The variance you are describing is genuinely one of the more confusing parts of SDIRA investing in funds, and the sponsor's timing explanation is usually the right one, though "usually" is doing real work in that sentence.
Here is what is actually happening in most cases like this. A bridge fund typically holds short-term loans. Interest on those loans accrues daily but may be recognized differently depending on whether the fund's books run on accrual basis (income recorded when earned) or cash basis (income recorded when received). The deal deck you signed almost certainly projected cash flow on one assumption, and the fund's accountants may be booking income on the other. When your K-1 reflects accrued but not yet distributed income, it can look like a mismatch even though both numbers are technically correct, just measuring different things.
The IRA wrapper does not change the K-1 mechanics. The fund issues the same K-1 regardless of whether the LP interest sits in an IRA or a taxable account. What changes is what your CPA does with it: in a taxable account, the K-1 feeds your personal return directly; inside the IRA, it matters mainly if there is unrelated business taxable income, which you would see called out as UBTI on the K-1 itself. Passive lending interest is generally exempt from UBTI, so if the fund is making loans and not using significant leverage, you may owe nothing and the K-1 flows through the custodian for record-keeping only.
The right person to get on a call with is the fund's investor relations contact, not the custodian. Ask them specifically: what accounting basis does the fund use, does the K-1 reflect accrual or cash, and can they walk line by line through the variance from the deal deck projections. A fund of any quality should be able to do that. Your CPA needs that explanation from the fund accountant, since the custodian genuinely cannot provide it.
For sizing the second position, I would hold on that until you have a clear written answer from the fund on the accounting methodology. Once you understand what you are reading, the sizing question gets a lot easier.
What does the K-1 show in the UBTI section, if anything? That would help narrow down whether this is purely a timing presentation issue or something that needs more attention.