Kitchen waste too high, is the only option to lower?

[DP]

If I went with the two products you posted, would this be the adapter I'd need: https://www.toolstation.com/diamond-core-drill-adaptor-sds-plus/p62181

It will
I have two, one with longer shaft.

You may or may not need a taper shank pilot drill too though I rarely need it even when core is 5” all the way from 28mm

 

[DP]

There's another adapter that includes a pilot taper, but it's SDS, not SDS+, so I don't think it's suitable: https://www.toolstation.com/diamond-core-drill-sds-adaptor-pack/p79014

This one would be my choice

Trap will be fine

 

[Madrab]

It was my understanding that if this is the case, the trap would be constantly full for the water to reach the waste outlet

The trap is always full of water anyway - that's the seal.

If you keep the outflow where it it, not only will the trap be full but 3/4's of all the waste pipework will be too. It will still drain but it's not right and needs fixed - that is why the last trap setup with all the tape and stuff leaked from multiple joints off the horizontal.

The outflow through the wall needs to be dropped to be inline with or below the final correct sink trap outflow level.

 

[foxhole]

The washing machine waste enters under sink too low to avoid syphoning. Buy an SDS from Screwfix , drill hole and return drill ( they accept returns no questions asked).

 

[Mottie]

Drill a new hole and be done with it!