....The Canon 300mm f/2.8L has an excellent reputation (as do most of the Canon L lenses) so why not buy a Canon 2x Extender? - Apparently they work really well together and depending on which body you use the compromise will be minimal.
I have had my Canon 100-400mm L II since February and it's extremely versatile and practical. The Sigma 150-600mm has a very good reputation too (better than the Tamron equivalent) but it is massive and very heavy.
I can strongly recommend buying the Canon 100-400mm II from HDEW. I recently dropped mine (don't ask!) and their help was outstanding, putting me in direct contact with Canon Approved Repair Centre A.J.Johnstone in Glasgow who turned it around together with my repaired 7D Mark II in 10 days including shipping. They put their technician in direct contact and kept me informed of progress and price. Everything was fully tested and recalibrated and cleaned. So, HDEW are a 'grey' importer - More like a very very pale grey! I approached
Park Cameras (where I had bought the body) and their response was poor by comparison and they would have remained a go-between without me having any contact with the repairer - I would not have even known who the repairer was! I have now bought several Canon camera products from HDEW who have premises in the UK you can visit - It's just not a shop and doesn't carry much stock.
This is HDEW's current price for this lens....
http://www.hdewcameras.co.uk/canon-ef-100-400mm-f45-56l-is-ii-usm-2980-p.asp
There's a thread on the forum about HDEW and it goes back years - Check it out.