Can you make a lump sum payment to the bank for the escrow shortage and then have the payment adjusted to account for the higher taxes, but not covering the additional escrow?

Good location, appreciation not guaranteed for the next several years.  895k asking price. 101k gross annual incomeExpenses: Insurance: $4,898Electric: 2,579Water/Sewer 5,085Fire Alarm Connection 708Property Taxes (if/when assessment is adjusted to sale price)-31,95130 Yr mortgage (20% down at 7.75%) 61,560Maintenance, Long-Term Capx, vacancy- 9,000 (this is probably a bit low)Total annual expenses: $115,781

If you do that, they can adjust your escrows back to normal. 

If not, what do you need to adjust to get back on track?

If you realize profit, sales price - purchase (and some adjustments for closing costs and capital improvements), you have taxable income. 

Your mortgage should have words to that effect.Either way, I would send a demand letter by certified mail for reimbursement of all your insurance expenses.

I am currently working to get certified in California.

There are far fewer ARM's (Adjustable Rate Mortgages) than there were in 2007/2008.

But, I will take your advice and will email and follow up with a letter, whether regular or certified.  

You must execute and then adjust when needed.