Tired of just lurking around on tis forum. Here is my thaught on how to resolve the issue - What I would have done.
You need two 3 major components: A custom integrator, that is able to reset itself, and a custom built mono stable flip-flop that has one extra input where voltage tetermines the holding time. Those two connects, and a back coupled inverted output (*) from the mono-stable flip flop to the reset of the integrator. * Probably need another monostable flip-flop that activates by negative flank to avoid integrator being disabled by reset input.