I did the Munda Biddi on my own in Nov 2012 but only as far as Manjimup as they hadn't finished the rest!
I didn't find pea shingle a problem to ride on (unless it got too deep) but it does have a high rolling resistance which saps your strength! Sand, on the other hand, is impossible. As you can't steer into a skid on a bike, you will fall off..... Which is another reason I favour pedals you don't clip into. Luckily, there isn't too much sand on the Northern part.
Now, as to how hard the trail is, somebody suggested to get a loaded bike and push it up the stairs. If you can do this you're good to go. And regarding how much kit to take, the suggestion is that if you can still lift the bike with all your kit on board you should be able to cope. But, you will pay in sweat and cussing for for all those pounds of things you thought might be a good idea but never use (and the extra helping of Xmas pudding around your waist). I had to manhandle the bike over a 5 foot diameter tree that had fallen across the trail just south of Karta Burnu. That was on the limits of what was possible for me.
One of the odd things I realised in retrospect is that you don't actually see as much of the countryside as you would expect as you are spending most of your time trying not to get caught out by the next soft patch, branch, hole, spider (in Aus, my rule of thumb is 'if it has more, or less than, two legs, leave it alone'), rock, etc...... Paradoxically, the times when you are forced to get off the bike are the times when you have an opportunity to take in the scenery!
I'd agree with the comment about only doing one 'stage' a day. If you are carrying all your own kit, and you're not as young as you used to be, that's enough, especially if the temperature creeps up towards 30C! On an unloaded bike you could probably do more but you'd probably want a support crew.
I shoehorned some fat tyres on a Specialised Crosstrail - had to modify the mudguards to accept them - and felt it worked quite well. Very glad of the hydraulic disc brakes on a number of occasions.
Speaking of which, there are parts of the trail which have obviously been designed by serious mountain bike enthusiasts. For instance, there is one section north of Dandalup where the track drops off the side of a road, downhill for a few hundred metres, along for a bit and then a hideous push back up onto the road. It might be mildly amusing on an empty bike but is not in the least bit funny when you have a load on the back. My advice, if you are intending to do the whole trail, is not to be proud and to take the short cuts if they offer themselves. And if there's a touring route marked on the map, there's probably a very good reason why!!
The official MB maps are pretty good but I'd recommend using a GPS as well. There are times when the signs are missing, the path has been moved for some reason, or you just missed a sign and got lost, when a GPS can save a lot of back tracking. I came across a junction after one diversion where there were 5 MB trail signs stuck together! Obviously they all pointed in different directions! Back Country Navigator on an Android smartphone worked pretty well. If you hunt hard enough you can find someone who has posted their ride for you to upload.
Lastly, forget the publicity pictures with all the cosy family groups. OK, some parts are family friendly but there are other bits which will lead straight to the divorce courts!
It's a fantastic trip which I'd thoroughly recommend but do expect some hardship!! Oh, and try to finish by the end of November or it is just too hot.
Michael.