Sounds like you need to use a sacylic acid type product to get rid of dead skin!

If you go to a beautician they can remove them for you. Honestly, those stubborn ones won’t budge without professional intervention and it will work out cheaper than buying cheap products that simply don’t work. It’s good to use those products for maintenance rather than removal.

I know what you mean. I think those blackhead strips only work on certain types of skin. My husband has very moist dewy skin and they work great on him, my skin is dry and so my black heads are a lot harder to come out.
I found if I used the strips the best way was to steam my face over a bowl of warm water first. Then wash it with a soapy face wash – nothing slippery or moisturising – and then use the strips. It really helps open your pores and get the strips to stick down well. I haven’t found much else helps other than gently squeeze with cotton buds

The strips are great for removing the gunk but then you are left with the open pores which simply clog up again.
To reduce blackheads is a bit of a process. As others have suggested a good and gentle facial scrub and giving yourself a weekly face mask should also help, There are masks out there that when its time to wash them off you can add a little water and use them like a scrub before removing.
I gentle toner might help also.
Do you find that you have an oily T zone? If so make sure you are using products for combination skin.

Have you tried a facial scrub? I use a clearasil scrub and have noticed a big reduction in black heads

I was going to suggest the blackhead strips, but as you’ve said they don’t work, what about something natural like a honey and cinnamon face mask, or a clay mask?