Hey Anakin Welcome to the Forums!
Im glad you are enjoying your time in Warp To Me.
Incursion Sansha is not like any other mobs you see in highsec. Triglavians included. These pesky rats are indeed more tanky than any normal rats out there.
5 light drones are actually doing very little damage to an Eystur, Renyn or a Schmael. Just gonna throw some numbers at you: im going to be generous and will say you have 100 paper DPS with your 5 light drones, which is a really high number for that. We are talking about 9000 EHP on those frigs. So even if you are not counting regeneration, travel time and damage application (which is a huge mistake xD) 5 light drones will take one and a half minutes just to kill 1 single frigate.
To be frank light drones are actually pretty useless overall in HQs plus they also die easily if they get any kind of aggro. Very ineffective. If it was me i would suggest that all the battleship should fly heavy drones exclusively in headquarters, using all the bandwidth they have. Some snowflake ships with 50 or less drone bandwidth are exceptions of course.
Now then what to do to kill frigates faster, right?
The answer is similar to how to overall upgrade site times, how to be faster, how to have better ISK/h:
Upgrade. Upgrade hulls and upgrade modules.
Learning the sites also helps. Taking roles, watching what actually happening not just brainlessly auto-piloting
For the DDD The upgrade part is simpler. When the person has the ISK for it get into an optimal vindicator fit with 2 webs and 2 tracking enhancers (the DDD instead of drone damage amp benefits more from enhancers, so thats different from the rest of the vindis). A vindicator has the potential to tear apart any frigate super-easily even without any lightdrones.
Now mastering the DDD piloting-wise can be an actual challenge. Takes a fair amount of experience, some hours actually doing the job.
But if anyone is interested here is some help from yours truly:
By the way about sites : yesterday we had 2 hours when we had almost 6 sites each hour ( 178 mil/h + LP ) and we had 30 minutes when we reached 226 mil/h + LP which in theory would have been a bit more than 7 sites an hour Speaking for myself i had some real fun for sure in those hours.
As you said it is highly dependable on competition and sites, but it also depends on how newbro the WTM fleet is overall which is really fluctuating. Sometimes can be a really rookie fleet sometimes not so much. As long as everybody is trying their best that is just fine.