GG,
I agree with the response above.
Consulting roles absolutely have time consuming and tough application processes (I went through legal training contract applications myself so have some sympathy with the time and effort required), BUT, they are still something that you'd be expected to simply fit in around your working life, whether that's mornings, evening, weekends, a quick hour of research over lunch etc... its demanding, but you have to find the time.
For perspective, at the firms you're applying to, there will be many consultants working 12+ hour days whilst juggling busy family lives and their own career development plans. Stepping down to some casual part time work will be very difficult to explain and an answer of giving yourself more time to devote to job applications is very unlikely to be viewed positively - I could only see it being viewed in a negative sense of "how will this person manage the pressures of the job if they think they are too busy now?"
Stay in the current role, accept that over the next couple of months free time outside of work and applications will be pretty limited until this years grad cycle passes, but it's all good development and worthwhile for your future career - best of luck.