That's what I indicated: At 'a few hours or a day' there are many problems which need solving, for which rates may be substantial especially given highly specialized knowledge.
But 'leadership' over some project, over any period of time, is not one of them.
A 'consultant to solve our DB limitations', sure.
But in terms of leadership, part time, non-business hours, no 'on site' (aka the OP has a 'real job'.). I don't think so.
$300/hr is a $600K/year run rate - is the relative cost of having for someone for extended periods.
A contractor can log much more than 1K hours per year - or less - it entirely depends on the nature of their work.
Also, some 'hours billed' are de-facto to the firm, not the individual. If you're hiring 'a lawyer' - you're really hiring 'their team' not really the individual, as often you would when hiring a contractor.
A good rule of thumb is to plan to bill not much more than 1000 hours per year, making $300/hr more like a $300K/yr gross income.