Neuschwanstein tickets,last minute itinerary change

It looks better from the outside anyway. Go to the bridge by public transport and enjoy the view.

There may be another problem, if the tours are sold out then logically it's a busy day. Last week we had reports of long delays on the Fernpass road (B179) on some days, obviously not everybody was going to the castle but it would be unlikely that the road would be quiet when the castle was mobbed (and vice versa). This is the only viable route for a direct drive from Innsbruck to the castle.

Live (so don't forget time zones) camera views of the road https://www.tirol.gv.at/verkehr/strassenbau-und-strassenerhaltung/webcams/webcams-bezirk-reutte/b-179-fernpassstrasse/ even at noon today (Thursday) the traffic was in a queue on the section with tight curves and police were managing the traffic at the Lermoos tunnel.

This is the only viable route for a direct drive from Innsbruck
to the castle.

Google Maps shows two routes that avoid tolls from Innsbruck to Neuschwanstein. One route goes through Austria (Reutte); it takes 1:55, according to Google. The other route goes through Germany (Garmisch-Partenkirchen, Oberammergau) and takes 2:01, only six minutes longer. I'm not cognizant of differences in traffic, but it looks otherwise like the route through Germany is a viable route.

BTW, the only tours of the castle are those conducted by the castle administration itself. "Secondary tour companies", if their are any, do not (cannot) run their own tours, They use the castle administrations own tours, so if those tours are sold out, it is unlikely that any secondary companies have any either.

Both of those routes go through Reutte, they meet at the north end of the village of Lermoos, see my comment about police.....

If I set a departure time in Google (so not Leave Now) for around 10:30 on Saturday morning Google maps is predicting driving times of up to 3 hours.

EDIT: I've been watching the B179 traffic cameras on and off for the past 2 hours (Saturday 13:00-15:00 Austria). The climb up from the Inn valley hasn't been too bad but when I started there was already very heavy traffic on the section between Reutte North and the Neuschwanstein exit, which is now spreading and runs from Reutte South beyond the Newschwanstein exit to at least the Füssen interchange in Germany and in both directions. According the Google Traffic the delay is 26 minutes- which is almost the length of an offical tour of the castle.

The Garmisch-Partenkirchen route does not go through Reutte, it more or less follows the same road as the 9606 bus. However, it will add about 30 minutes to a drive from Innsbruck to Fussen.