I checked with my uncle (who stay in sirsi) and my dad (who stay in ankola) both travelled in these routes upto sirsi and ankola last week.
If someone visit Jog Falls take this route:
Bangalore -> kadur -> Shimoga -> Sagar -> Talaguppa -> Jog Falls -> Mavinagundi -> Siddapur -> Sirsi (500km) -> Devimane ghat -> Mirjan -> Ankola -> Karwar -> Goa(700km).
If you don't visit Jog Falls and go directly to siddapur from talguppa you can save 20km. i suggest you stay in shimoga (jewel rock is good hotel) visit Jog Falls and then proceed to goa.
this route is just 50km extra comapred with shortest routes.
kadur -> Shimoga around 40 km bad stretch.
Talaguppa -> Jog falls -> Siddapur around 15km bad stretch.
devimane ghat excellant (carefull about sudden turn and 2 or 3 big photholes thats all.) KSRTC/Tempo drivers are worst these area if they see outside registration vehicles never give side.
8km after devimane ghat you get right turn singel lane excellant (courtesy honest and hard working ankola MLA

) road which join nh17 in mirjan.
from mirjan you get small bad stretches every 4 km. big big photoholes.
Shortest routes are ->
1. blre -> shimoga -> Honnavar -> karwar -> goa
2. blre -> chitradurga -> haveri -> sirsi -> karwar -> goa.
but bad roads between chitradurga -> haveri -> not smooth road to sirsi.
from jog to honnavar road is not good as well at least for 20km.
so best route right now is
Bangalore -> kadur -> Shimoga -> Sagar -> Talaguppa -> Jog Falls -> Mavinagundi -> Siddapur -> Sirsi (500km) -> Devimane ghat -> Mirjan -> Ankola -> Karwar -> Goa(700km).
and its scenic route. watch out for Bikers because they don't have any idea how to cross the road and they go all around road with nearly 3 digit speed.
also taking right turn from NH 206 to siddapur road, left turn to kumta road before enterring sirsi from siddapura, right turn to mirjan after devimane ghat confusing points. make sure you ask locals in kannada for directions.
Regards,
Ravi.