There are lot of options to consider, even with an amp like this, the SR-007 Mk2 will have more bass slam the the detail and imaging are on a whole new level, Lambdas just can't reach to those heights. It is a very different sound overall, but a decent match with the modified 727, which I think is a bit brighter and flatter than the hybrid Stax amps with tubes which do a good job at "rounding off" Lambdas, but not as dynamic.
They seem to be going for fairly decent prices used, an SR-L700 Mk2 costing more just shows how much Lambdas have gone up in price.
Also, if you change to a balanced source you become less dependant on cables (better noise rejection), the Stax amps (including the aftermarket amps) are inherently balanced by design, so you are eliminating an unecessary unbalanced->balanced conversion with that (you also get +6db gain which is set lower on the 727 compared to other amps) for me it becomes a bit warmer and more dynamic, a positive change.
Some people are driving a top-tier headphone with a mediocre amp that sounds congested but overall still on a much higher level of detail and imaging, while others do it the polar opposite way, and it is quite difficult to evaluate, which is best.
But whatever you get first, you might end up upgrading all three things, in which case, it is quite a huge jump in price (but also sound quality) people can only really argue about what's the best order to do that (and more crucially, where to "stop")
If you intend to stay with the L300LE, then the KGST or an SRX+ should be decent upgrades without going higher to a Carbon or a BH, as long as you find a good builder for them.
