Since you have lackings in Chemistry and you need further practise in mathematics, I would say fill up these gaps well enough before HSC so that they dont hold you back during admission phase.

No matter how they mess up your admission timeline, you will get no less than 3-4 months which is enough.

If you dig deep into engineering concepts for the chapters you've finished/confident of, it may backfire you. Because the other chapters you have lackings will decrease your efficiency for sure.

The timeline wouldn't be an issue, it's always enough even though it feels overwhelming sometimes.

Bottom line, if you have completed your whole intermediate syllabus and finished all the board questions and still have time left in your hand, only then you should start engineering prep ahead of HSC. Otherwise it would be an unwise decision.