Dear Ashwini,
No worries you can perform the similar pooja in Tryambakeshwar ( maharastrastra ) and the pooja name is Narayana Naga bali pooja. Even this would be for 3days for nagabali and naryana bali might also would be done at the same time. And this pooja shouldnt be done on Dasami, Ekadasi, Astami, Gokulastami, Sivaratri, Solar & Lunar Eclipse. If you perform this the no requirement for you to perform once again in kukke subramanya.
Regarding other remedies of throwing charcoal there is not any specific timings only see that you wont throw that in early morning during sunrise.
GOD BLESS!!!
Srinivasa Temkar