Hey guys, just offering my two cents on the matter.
Generating power in Muay Thai is a complex technical mix of factors and of course there is no substitute for volume and practise on the basic strikes (more volume than you would believe) especially with a good pad holder and a lot of time spent on the heavy bag. Sport specific training aside, the main driving forces behind strikes, in particular kicks and knees are core rotation and hip extension. A good roundhouse kick is a blend of both whereas a long knee or front kick involves mainly hip extension (hip hyper-extension to be exact). To be clear, the rotational aspect of a strike (including punches and elbows in this instance) is less of a twist and more of a full body rotation, that is hips and shoulders working together.
With that in mind, any movement that involves bracing the midsection, especially the antirotation forces involved in a one armed swing, as well as those promoting powerful hips extension such as one or two handed swings will have great carryover towards strikes in Muay Thai.
In short, there is no substitute for repetition of technique, on pads and on the bag, but as a supplement to technical training a schedule like S&S is ideal. If it's not going to flatten you and mess with your recovery adding a moderate number of close grip push-ups (or plyo push-up) as well as chin-ups will take care of a good amount of your strength and conditioning needs for Muay Thai.