We are trying to find a want to hike this route without killing ourselves.
ONe suggestion was to overnight in Griesalp.
Does anyone know how much hiking and gain there will be on either of these hiking days and whether or not we can take a cog part of the way? A travel guide has told me there are no short alternatives? Is it better to just take a train form Murren to Kandersteg?

You will find lots of information on this---photos, trail descriptions and profiles, if you Google "Alpine Pass Route Mürren". From Mürren you climb up to Sefinenfurka at 2600 meters. Back down to Griesalp at 1200 meters. Then up and over Hohtürli, at 2778 meters the highest point on the Alpine Pass Route. From there down to Oeschinensee (1600 meters, I think) and then to Kandersteg (for that part there is a lift if you want). There is no lift or train to cover the other sections of this route. It is considered the most difficult section of the Alpiine Pass Route---note one website with photos of the steps down from the Sefinenfurka. Most people do it in two days (overnight at Griesalp) or even three (overnight at Rotstockhütte and Blumlisalphütte). But all the information you need is on the web.

I should clarify one point. You can, if you wish, do half of this hike by taking a postbus to Griesalp (from Reichenbach im Kandertal on the train line). Then hike from Griesalp over Hohtürli, etc. Or from Mürren you could hike to Griesalp and bus and train to Kandersteg from there.

Does anybody know of any affordable and reliable hut to hut hiking tours in the region? I'm considering this route as I'm having difficulty putting this together.

Here's a book that was recommended on one of my threads. I ordered it. Hope it helps you.

Swiss Bernese Oberland: A Travel Guide with Specific Trips to the Mountains, Lakes and Villages, Third Edition
Philip Alspach and Loretta Alspach
Paperback: March, 2004 (Intercon Publishing)
ISBN: 0963223577

Krissy, Before planning our first trip to Switzerland I considered using this company: http://www.alpinehikers.com/

They will plan a "self-guided" tour for you and make all the arrangements. I decided to do our own trip instead, so I never used them, and I can't say if they are reliable or not, but I liked their philosophy. However, these tour operators all seem to charge around $200 pp/pd or more, and you can do it yourself for a whole lot less than that.