I'm really liking my new position so far. As I said before, the saddle is approx 2cm higher and 1cm more forward. I feel like it's easier to grab the bars further out and to bend my elbows a bit more without rotating forward (unsure why this is, as my reach should be exactly the same). My legs also feel less "cramped" while riding seated for long periods of time. Before I would have to stand occasionally to stretch them out, using mostly hamstrings. Now I feel like I'm using the muscles more evenly, although I can sense I have a bit of tension behind my knee from having to extend further.

Back to the handling thing...

My former (we didn't see eye-to-eye on some personal matters) coach was a former professional, Junior National Team, Team Director, NCC and NRC racer, etc etc. He told me to think of cornering like riding a unicycle. Weight bias is generally on the rear wheel and steering input is done through the hips. To relate this more realistically, the front wheel is mainly for stability. Theoretically, by this thinking, you could perfectly navigate a corner without touching the handlebars at all. He also suggested that during an especially tight or hard corner, weight bias should be shifted backwards and center of gravity lowered. With the weight bias on the rear of the bike, proper countersteering measures can increase angle of attack without increasing lean angle of the bike, in theory increasing traction over a greater degree of cornering effort.
There is also the benefit that, in the event of lost traction, the bike tends to drift before it full out slides. Of course, this increases the risk of a high-side crash, but it also increases the likelihood the bike can be saved. I've experienced corners where both the front and rear tire were skidding, without falling down.
This doesn't come without downsides, of course. In the event of a severe loss of traction, the result is total system failure. Both wheels wash out simultaneously and there is nothing the rider can do to remedy the situation. This is a slight contrast to a forward weight bias in which the front wheel washes out.
Also, with a rear weight bias, the sliding rear wheel can be treated as a tool, rather than a problem. By temporarily unweighting the rear wheel, the rider can initiate a slide and then return weight to the wheel when they are ready to resume power. This is much more commonly seen in mountain biking and cyclocross than road riding, but I have used it at least once.*

*During a spirited group ride (this particular ride encompasses 3 individual mini races and the riders treat it very much like a race), coming into a left-hand corner approx 800m from the finish @ about 25mph. I was about 10th wheel but wanted to try for the sprint. I left the group and went to dive bomb the corner, accelerating to just below 30, right as #3 rider had the same plan. He cut in front of me and hit my handlebars with his hip. (This as we're entering the corner). I weighted the front end, grabbed a handful of rear brake, and fish tailed through the corner ending up right on his tail to take 2nd in the sprint. I'll admit, none of this was done in conscious thought, but rather more like something of a flash back to riding bmx as a kid.
All-in-all it ended well, and it certainly could have been a very dangerous crash at that speed.