Is it better to use red or red-orange LEDs to increase the CRI of a cluster of neutral white LEDs?
I can answer this question, since this is a subject I looked into in great detail.
Actually you could use a wide range of different possible wavelengths. Any of them would increase CRI, especially in the red area, and whether you go with a longer (red) or shorter (red-orange) wavelength has its own unique advantages and disadvantages.
The first thing that needs to be said is that if you simply add red to white, you are not going to have white color light. You are going to have pink-tinted light. The human eye is very sensitive to small color tints and color shifts.
But let's ignore that part for a moment and get to answering your question.
You can use a wavelength as short as 615nm, or as long as 660nm. Actually it depends somewhat on the CRI of the white LED to begin with. If you are using a very low 70 CRI white, and the color temperature is somewhat high >4000K, then something like 615nm is going to give a greater CRI and efficiency benefit than it would in other situations.
The human eye is much less sensitive to longer wavelengths, so the amount of red light added is going to be significantly (several times) greater at 660nm than it would be at 615nm.
I have played around with this and found that 650nm still gives excellent red color saturation, and is almost twice as efficient as 660nm, due to the rapid drop-off of human wavelength sensitivity. In fact the only reason to choose 660nm is if you are trying to go for an unnatural saturation of red.
635nm is also an excellent compromise, and gives pretty good color rendering overall, although is probably not going to bring you above 94 or 95 CRI.
Something else I have noticed that is very important - if most all of the red wavelength light is coming from the red LED, then if you use a wavelength that is too long, it is going to make skin tones look unnatural. Skin tones will not be as brightly illuminated (meaning they can still appear a little dead grey) and will also acquire an unnatural pinkish tinge, rather than a healthy orange glow.
You see, the problem is that you cannot up the amount of 660nm light to a level that will properly illuminate skin tones without it overdoing the red saturation on other red colors and throwing off the color rendering balance. The ideal red-orange for a healthy-glowing skin tone is about 520nm.
When you have a "high CRI" white LED of about 91 CRI, then the spectrum will be high in 620nm orange-red light, and so it will illuminate warmer orange-red colors well, giving their appearance balance, warmth, and life. But the deep red colors will still not be rendered the most properly and will acquire a more orange tinted red than they should.
If you are using an 87 CRI white LED, then 650nm is an appropriate choice to go with it. Especially at higher color temperatures at 4000K or above. At a lower color temperature (say 3000K) or if using a lower CRI (say 80 CRI) white LED, you may want to go with 640-645nm red, or perhaps even a mix of 620 and 650nm LEDs.
So it depends on several factors. The CRI of white LED that you are using, the desired final color temperature range, and the desired CRI level that you need to obtain.
I think "neutral white" is usually 4000K (sometimes 4000-4500) so in that situation I think 535nm is probably the wavelength of red you would want to use. To more specifically answer your question. It should be able to take your 80-85 CRI and bring it up to the equivalent of maybe around 93 or 94.
The amount of red you will want to add is really not that great. Maybe in the range of 7 to 11 percent of the total light.