Saturation is a magnetic thing, not a thermal thing. (Well, it's affected by temperature -- but it's not a power loss, not at these frequencies.)
It's a reduction in the inductance at high current, that's all.
A gap would work, but ferrite is a ceramic. You have three problems:
1. What do you cut it with? You need a carbide abrasive. (A cutoff wheel would work.)
2. It's very brittle, so you might chip or break it in the process. If nothing else, it's more likely to break from handling, or other stress.
3. How much gap to create? (This can be calculated, at least!)
Usually a different core shape is used, like an 'E' or rod or bobbin type. These can be gapped (by adding an insulating shim), or are natural air gap shapes (a rod or bobbin is half air gap already!).
Powdered iron cores and ferrite shapes are commonly found in various equipment, or are affordable from various suppliers.
The thing is, you probably don't have any means to assess the RF performance of this filter?
If that's the case, then, the added series inductance doesn't matter -- for all you'd know, it could be a link of wire, right? Which begs two further questions:
1. Do you really need honesty in the construction of a device which does not serve an honest purpose?
2. What ultimately is the purpose of this device? If it is to perform its stated duty (RF filtering), then you must have some means to test it, right? If you don't know whether it will work or not, and you can't determine whether it's working or not, why bother with it at all?
This unfortunately collides with a value at the heart of audiophile culture: that double-blind testing, or indeed much testing at all, is not only useless but counterproductive. Understand that, while we can offer technical solutions here, within that culture, they're just a bunch of hot air... Point being, #2 may well have a positive answer (why bother? because: ...), just a non-technical reason.
Tim