What does your paid preparer think?

I think this is beyond your capabilities.

I'm trying to find out if there is possibility to increase the asset in books and also increase it in the tax return to take advantage of a higher depreciation. Not sure if that is allowed by IRS. I have not asked an accountant.

You cannot depreciate the increase in value

You have asked (here) 1,000s of accountants.  You should find a local professional to work with who will learn the intricacies of your biz, and do returns right.
My new client used TurdoTax (tm) to prepare 2017, and misunderstood what she was doing.  Under-reported $36,000.  She does 1 return a year so she cannot be expert in the software.
I do hundreds a year (for 30+ years, after an Accounting degree - then all those years of continuing education).  

Therefore, the historical value or beginning value is the only value that can be depreciated?

Point proven!

Thank you so much!

@esther.realestat

You track your Costs. That is Basis, or Your invested value. The "original" value as cost, and any qualified improvements should be tracked as your Basis.

This is why you need to consult your own Tax Professional. You are confusing Fair Market Value and Your Value.