I know this is an old string, but I haven't checked it before.
You've probably bought a capo since the recording, too. Nevertheless, I tell you what I've experienced in the capo field. Others might benefit from it, too.
I think a capo is good if it's light, quick to use and doesn't stick out of the neck, in this order. A heavy neck is awful...
It should, however, match the width of the neck and hold the strings down firmly as the starting point.
I use the simple Dunlop crocodile jaw design. It's a bit on the narrow side, especially in higher positions (such as VII), but still it's the best because it is the lightest, the firmest, the smallest and the fastest to use when you have other things on your mind. You need two hands for the fixation, but only for a short time. It has only a strap that goes around the neck, but it's never hurt my finish yet.
You can consider flamenco capos, they are very natural (wood, bone, leather, &c.), very light, very firm-gripped, very fancy, but fussy to use (position change is a slow process, you need two hands for a longer time). The good ones are expensive, too. I have a very beautiful one, but rarely use it - its proper fixation is a slow process (compared to the Dunlop design).
From the more modern designs there's the one which holds the neck exactly like your index finger and thumb in a barre, and has another, third lever underneath with a tiny roller. This is to fix the 'barre' on the neck. This type is extremely fast, sleek-looking, but it can be weak-gripped (especially if you don't adjust the setting screw as you go back down the neck), and a bit on the heavy side. And they still jut out a bit from the neck which can hinder your hand's free motion in certain positions. This is the ony one, however, that you can actually fix - and move - with one hand, if you are experienced.
There's the type which looks like a barre again, but with a very short 'thumb' only, no third lever, and the 'thumb' has a screw with a big head, which sticks out to one side of the neck. It is light, doesn't project much, quite firm, sleek-looking, but you, again, need two hands and some relaxed time and concentration to fix it properly. And, it's aluminium, which is light, but not a very 'musical' metal.
I think you can forget the other designs because of their disadvantages.
If I were you, for the renaissance pieces I'd try capoing up to 3rd position, maybe 2nd, to gain more brilliance. If the sound is better, then you've gained something, if not, you can always forget the capo.