My vet only offers ‘hygiene trims’ and does this under anaesthetic. And they’re a specialist rabbit vet – but still don’t offer any type of ‘grooming’ clips. Check out youtube for how best to clip – some really good ones on there. I’ve got an English Angora and he too gets these mats right up close to his ears. I gently tease them out as best as I can and then use sharp but blunt tipped scissors and snip super carefully. When they’re too close to the skin, you need to wait a little for them to move out and then gently tease with a brush.
I don’t have a ‘grooming table’ either. I just get on the floor with him. He’s great though – tends to sit super still when I do this.
I actually found that the best brush for my bun is one by Great Lengths – it’s designed for hair extensions and it’s got silk tipped ‘points’ so it’s not too sharp on his skin but really gets into the guard coat.
Good luck – mats are a nightmare. We brush our boy daily and yet he still gets them. Once winter has passed, our boy will be getting an actual clip all over!