Divergence is a yin-yang reality, it is the size of the diode emitter and the focal length of the collimation lens together which produce a given divergence, neither alone fix it to be what it will be. Due to this, the diode you already bought might be just what you need, if using a longer FL lens or beam expander:
So far, I have not seen a high power low divergence red laser diode, for that matter, any high to medium power single emitter laser diode (as laser diodes go) which produce low divergence without using larger diameter collimation lenses to make up for it. I understand you are looking for the best trade off of power to divergence, but I believe you likely won't find a diode which will suit what you want well enough, not at that wavelength, unless you don't mind a fat beam.
If you use a long focal length lens to collimate the beam from your laser diode, or a beam expander with your laser, the divergence can be fairly low, even for red (which unless a low power single mode diode, all red LD's have relatively high divergence). If I were looking for the highest power lowest divergence nicest looking laser beam from a diode at any wavelength or color, for a pointer I'd just go with the highest power single beam diode you can find and then if the divergence will be too high, decide on either a larger longer focal length collimation lens, or adding a beam expander on the output.
You can simply add a 10X beam expander to what you already have and end up with what you are looking for far easier than redesigning the whole pointer, but using a beam expander comes at a cost; reduced output. However, if using a quality beam expander with low loss AR coatings on the optics, the loss isn't so great as to make much difference, not a difference you will be able to see.
If you want to start over, or re-engineer the pointer, instead of using a beam expander, collimate the beam with a single large diameter long focal length lens and the output power will be a bit higher than you would have if first collimating the output with a smaller lens, and then putting a beam expander in front.
If you use a long enough focal length lens to collimate the output of the diode with (which will produce a larger diameter beam), for laser pointer use (not burning) it is fairly moot if the beam is corrected to be more square or not because if the beam is expanded enough (no need for a BE in this case with the added loss) both axis will diverge so much slower the beam will remain tight for as far as the eye can see, without turning into a sky rake, as is normal for all red laser diodes, unless a single mode diode and even they have too much of a rectangle for my taste.
Power for power, red is already a wavelength the eye is less sensitive too, although not so terrible at 638 nm compared to 650 or longer, but in either case to have a bright appearing beam you really need as much power as you can muster, which I believe is what you are wanting. Only thing is, if you use a long focal length lens to collimate the beam with, or a beam expander after collimation, you will have a fat beam, which at close range won't appear as bright, but in the far distance will remain as bright and not fade out nearly as fast as a thin high divergence beam would which spreads very quickly.
Note: If buying a beam expander, make sure the input lens diameter is large enough for the beam diameter you will be shooting into it, and that at whatever X factor the unit is, multiplying the input beam diameter does not overshoot the diameter of the beam expander output lens too. You need to find the actual specs, some beam expanders may have a 5 mm input lens but only allow a 1.5 mm diameter beam at the input without either being clipped at that input, or cut off at the output lens and result in a large loss of power. Also, make sure the lenses have AR coating and that the coating is for the red wavelength, in this case.