How to control RMS output of an DC-AC inverter?
Yes it should be possible.

A 115Vac waveform has a peak voltage of 162.6V. If you assume an ideal inverter (no volt drop due to conduction or deadtime on the inverter..), the peak output voltage that can be generated is 270V ~ 190Vrms single phase waveform.

I mention single phase because this is key. A 3phase, 115V phase voltage rectified would produce ~270V and thus if you wanted to re-invert back to 115Vac you are now entering into the world of ideal cases. 

Lets proceed with a DC-link of 270V and a need to generate single phase 115Vac. This requires a modulation depth of 60% ( \$ \frac{\hat{V_{o,pk}}}{Vdc} = \frac{115\cdot \sqrt{2}}{270} )\$

Consider an inverter as such:


This produces an output like:


Which meets your stated needs. There is plenty of margin in your modulation to overcome real-world drops: output semiconductors, deadtime, output filter. 

It is stated that you are achieving higher than 115V output. The simple option is to reduce the modulation depth but it is worth investigating why it is higher. It is possibly due to light loading, higher DClink voltage than you expect or measurement error. 

This is purely open-loop an will only generate a sinus PWM pattern. The actual output will be dependant on the DClink voltage: if there is a significant AC component then this will appear on the output waveform 

A 20Vpk disturbance at 1/2 the output freq:



To resolve this you would need a closed-loop controller either around the DCLink or the output AC to provide additional corrective factor onto the PWM pattern.