I've had a couple of bike trips through the highlands that cover a reasonable amount of the F-roads you describe- your trip is all doable, just allow plenty of time for weather holdups and for slow travel on some of the rougher roads- the Icelandic wind in particular is a force to be experienced!
Sept 2016 my wife and I biked from the south via the F261/Reykjadalir/F225 to Landmannalaugar then north through the Sprengisandur on the F26. Sept 2017 we came back mainly to ride the Gaesavatn Route in the north (but also managed a bit more)- we rode the F88 to Askja/Dreki then on the F910/Gaesavatn to Nyidalur and back out to Akureyri via Laugafell. This took us 11 days including a rest day in the pool at Laugafell- distance per day was never a focus for us as it was more about safe travel- each day is a bit of a dice roll with the weather. The Gaesavatn south of the F910 is also pretty rough, very remote and hard travel so you don't really want anything to break!
In 2016 we has a bit of trouble with flooded rivers south of Landmannalaugar but I don't think these would be a problem in fine weather. There are some glacial rivers to watch out for on the F910 and north of Nyiladur on the F26- in 2017 we were lucky and found these easy to cross (probably something to do with subzero temps and snow at the time!) but they can be difficult to cross depending on the snow/ice melt. Crossing the Dyngjusandur desert and the Vatnajokull glacial outwash plain south of Dreki can also slow you up/stop you in the wrong conditions.
We found this online guide gave a good rundown of the various highland routes (written 2005 before the Iceland tourist boom but not a lot has changed as far as the highland roads go):
http://www.masterlyinactivity.com/ivan/iceland-zones.html If you are interested I wrote a summary of our trips on the Ground Effect website:
https://www.groundeffect.co.nz/blogs/news/an-icelandic-rabbit-hole