Be careful that pride is not getting in the way of making a good decision. As it stands now what difference does it make to have 200K worth of debt and a 200K house or 225K of debt and a 250K house? Sure you would have a 25K higher net worth, but is that really important? Some may even argue that such an increase is not real as equity in primary residence might not be a good indication of wealth.
While there is nothing wrong with sitting down with a banker, most are likely to see your scheme as dubious. Home improvements rarely have a 100% ROI and almost never have a 200% ROI, I'd say you'd be pretty lucky to get a 65% ROI.
That is not to say they will deny you. The banks are in the business of lending money, and have the goal of taking as much of your hard earned paycheck as possible. They are always looking to "sheer the sheep".
Why not take a more systematic approach to improving your home? Save up and pay cash as these don't seem to cause significant discomfort. With that size budget and some elbow grease you can probably get these all done in three years.
So in three years you'll have about 192K in debt and a home worth 250K or more.