I would suggest you make your application for ILR now. I appreciate you have an unspent speeding conviction, however, the UKBA will normally disregard a single conviction for a minor offence resulting in a bind over, conditional discharge or relatively small fine or compensation order, if a person is suitable for grant of leave in all other respects. By 'minor offences' it means speeding or other 'regulatory' offences.
Offences involving dishonesty (for example theft), violence or sexual offences are not classed as minor offences. Drink-driving offences, driving while uninsured or disqualified are also not minor offences.
Thus, if you were found guilty of speeding, this would constitute a minor offence.
In any event, if your application for ILR is refused, you would then have sufficient time in which to apply for Further Leave to Remain if you had to.
If you wish to discuss, please feel free to ask further questions.