I've never through-hiked the enchanments, although I assure you it is definitely up there on the bucket list. If you're going later in the season when there won't be snow up Aasgard it should be a fairly straightforward ascent. If there is snow, more equiptment and training could be necessary, but assuming favorable conditions the training for this sort of thing would probably be farily straightforward. For training I would definitely reccomend a mixed set of cardiovascular and strength training throughout the week. If you feel confident in strength or vice versa one could always focus more on one or the other. When you have the time, definitely go for long hikes with a weighted pack. Nothing gets you in pass-climbing-shape like doing runs (by runs I mean grueling slogs) up Si with a couple of gallons of water in your pack. If you can hit your target weight on those sorts of hikes, and you are focusing on building cardiovascular endurance and strength throughout the week, there's no reason that you should see results over the long term. Doing backpacking trips of similar length and elevation gain will also help with this. Finally, it just comes down to your will to succeed as you switchback up the pass, and if you've made it that far, don't doubt you can make it further.

"Not getting to the summit is not failure, it is an opportunity to go there again."
-Kilian Jornet-