The main desirable trait of this thread is the general admonition to be careful and cautious ..
I feel capable of slowly increasing thrust to try and solve that problem (my emphasis) ..
RAT 5's comment should be read carefully by all as it is written in blood. The certification animal doesn't look at thrust increases during a dynamic manoeuvre.
As a f'instance, an aeroplane with which I had some familiarity in a previous life had a reasonably well-behaved static Vmca and, indeed, could get to significant yaw angles. But life could get interesting in the dynamic situation.
I was involved in the on-site investigation of a fatal which (almost certainly - based on eye-witness debriefings) involved one of the pilot's panic advance of one throttle as the aircraft was about to impact the takeoff overrun. This particular aircraft had extremely good engines (very high mod status embodiment) and the thrust response, quite rapidly, saw the aircraft yaw/roll significantly and cartwheel after the wingtip impacted the runway strip end. (There were some related things which made the pilots' job much more difficult than it ought to have been but the thrust/yaw/roll/crash/burn/die exercise was, nonetheless, very obvious and devastatingly effective .. ).
If you elect to increase thrust (I'm not suggesting whether you should or should not) .. do it slowly so that the asymmetric effect can be assessed more easily and the requirement for rudder input adjustment made with some degree of confidence.
As an aside, the B707 report is worth reading to note the importance of bank angle on Vmca ..