Sounds like you will need a BEC to bypass the ESC for power. What receiver are you using? You need to make sure it can handle more than 6V as well or the wiring gets a bit more complicated.
Even if you increase V from the ESC via settings, that won't increase current, which is probably why your seeing a "brown out" when you try to move the servo. It seems it needs more current than the BEC in the ESC can supply.
If you have the HPI Blur F360C, that's a rebadged castle ESC, the Mamba Monster V1. I had that one first and swapped it out for the MMX as the MMv1 isn't waterproof. I can't recall if the BEC is adjustable in the MMv1. I took a look at my printout from when I adjusted the settings and I had the BEC set to 6V. I suppose if I get some time later today, I can dig that ESC out and plug it into my PC and see if it's adjustable.
However, it's pretty well known that the BEC's built into castle ESC's tend to not be overly robust. Why, I don't know. I guess they like to nickle and dime their customers and get them to buy their external BEC as well as the ESC. Personally, I don't care for using an external BEC as it just adds complication and more junk to go fail and jam into an already small receiver box on many vehicles... but you do what you have to do.
From what I can see on HPI's site, the
BLUR (part# 100684, castle MMv1) was replaced with the
ELC-6S (part# 113126, guessing castle MMv2) which was replaced with the
ELH-6S (part# 120021, rebadged hobbywing), so I'm pretty sure if your says "blur" on it, it's the castle MMv1 ESC and you need the castle field program card or USB link to update it. Go with the field card as it can be used as a USB link as well.