After writing my comments, I started writing a new answer. That got long, so here's a shorter one.
The "energy of an orbit" may be poorly defined and depending on the definition, is not subject to energy conservation laws. Let's ignore it and focus on the kinetic energy.
Kinetic energy is not necessarily conserved. Momentum is. Momentum (derived ...
The sum of all mechanical energy will be the same after your ideal burns. The difference will be that the portion given to your exhaust will be greater for higher burns.
For a burn farther away from the planet:
The craft will be higher, so the PE of the exhuast will be greater.
The craft will (usually) be slower, so the KE of the exhaust will be greater.