How about considering the possibility that whenever there is an 'exp-bonus
day', the exp would not be doubled, tripled or so.
Instead, all monsters would give a lot or maybe very lot experience during the
time. Fox example, with this exptune monsters would give a lot of exp (or
more) until the boot and after boot the tune would change normally.
Remember, not every player is able to play straight from boot and -believe or
not- not every player are able to exp here 24/7. This would just tie the odds
amongst players and give players a change to exp with good rate all day.