HELP! Masters in Accounting and Data Analytics? Please HELP and give honest opinions

Hello,

I am a senior at a top 10 accounting undergraduate program. I have done multiple internships with a big 4 firm and that big four firm just offered to pay for my Masters in Accounting and Data Analytics before joining their tax practice for mandatory three years (or else I have to pay them ~30k back). My goal is to eventually find my way to private equity/investment banking and I would want to do investment banking before breaking into PE. I take Level one of the CFA in December and hope to have the CPA completed by April 1st (I'll have 150 hours) before taking Level 2 of the CFA in June.

Ideally, I could work for a year under the big four in order to satisfy my work experience requirement to become a licensed CPA. Another plus to working a year in accounting instead of going straight to investment banking is that I will be able to study hard enough to get a top GMAT score in order to eventually get accepted into a ~top 15 MBA program and to prepare and sit for L3 of the CFA (much more time than if I was an IBanker). After this year or year and a half, I would hope to switch to IBanking for 2+ years before going to get my MBA. All of this would be without a MADA degree.

The problem is the firm will not let me come work for them unless I sign their 4 year contract (1yr. school and 3 years as a tax accountant). The pay is good with this firm and work-life balance is also a plus (max 65 hours and that would only be a couple of weeks out of the year). Top MBAs are also extremely expensive. UVA, for example, will end up costing ~180k after taking cost of attendance into account. I would be in debt at thirty vs having some accumulated wealth if I simply had the MADA. By choosing the MBA route I am betting that I will have caught up with the wealth that I would've had with MADA by 40 at the latest (tons of variables, but you get the idea).

Note: I have around a 3.9 and hold/have held a couple of admirable positions around campus.
I am not open to the idea of doing audit.
Getting a MADA degree then an MBA is not on the table.

All that is to ask: 1.) Could a MADA degree actually get me into private equity at some point? (Assuming L3 of the CFA and the CPA is passed)

2.) Is an MBA (lets assume UVA Darden) really that much more powerful in IBanking/Private Equity than a MADA degree from a top 10 accounting program.

3.) Would IBanks look down upon me if I were coming out of a small hometown accounting firm (vs. big 4) for an analyst position after a year and a half vs. right out of college. In my mind I have it that it is easier to come out and get a job because there are college recruiters and youth is an asset that firms generally value.

4.) If I get an IBanking job and they want me to start in June, I know deep down that there is a chance that I do not get a phenomenal GMAT score, I will not be able to get my year of work experience as a CPA, and L3 of the CFA will be a serious challenge. Should I still apply at places and just ask them if I can take a year off to accomplish all of these things?