Correction of amplitude after zero padding for upsampling purposes
If you use an 1/N normalized DFT, then you shouldn't have any problems with your amplitude when you take the inverse DFT (with no normalization factor/factor of 1).  Consider the case of a pure tone with a whole number of cycles in the frame.  Only one bin pair will be non-zero.  No matter how many extra zeroes you insert, the inverse DFT will reconstruct the same signal in the same duration, just appropriately upsampled.  The amplitude of the signal will be twice the magnitude of of each bin value independent of your sample count.

If the normalization factors are already hard coded in your routines as &quot;1&quot; forward, &quot;1/N&quot; inverse, you can simply use them in reverse roles.  Take the &quot;inverse&quot; of your signal, zero pad it (splitting the Nyquist), then take the &quot;forward&quot;.
Alternatively, just multiply your final results by a factor of $\frac{N_{new}}{N_{old}}$, which confirms your observations in the update.