How to linearly boost the output of a Gaussian shaping amplifier?
A high speed opamp will work. This is the fastest that I have in my stash. https://www.ti.com/lit/ds/symlink/lm6171.pdf Probably overkill.
It will pass a 1 \$\mu\$s squared pulse with good signal integrity, so a shaped pulse should be no problem.
This experiment has a gain of 2. You will need to reduce the value of R2 to get the 10/6 ratio that you desire.
You will want to add two 0.1 uF decoupling caps from the power pins to ground, close to the IC.



simulate this circuit &ndash; Schematic created using CircuitLab
Yellow is the input, blue is the output.