Does this kind of meditation have grounding or an equivalent in Buddhism?
OP: Then try and notice any attachments or aversions that I feel in the moment.

This seems right:

the latent tendency to lust reinforced by being attached to pleasant feelings;
the latent tendency to aversion reinforced by rejecting painful feelings;
the latent tendency to ignorance reinforced by ignoring neutral feelings;

Pahāna Sutta

OP: ... Allow the aversion to be there ...
OP: ... Allow the attachment to be there ...

I believe you have to remove attachment and aversion:

If he feels a pleasant feeling,

he understands that it is impermanent;
he understands that it is not to be clung to;
he understands that there is no delight in it.

If he feels a painful feeling,

he understands that it is impermanent;
he understands that it is not to be clung to;
he understands that there is no delight in it.

If he feels a neutral feeling,

he understands that it is impermanent;
he understands that it is not to be clung to;
he understands that there is no delight in it.

If he feels a pleasant feeling, he feels it in a detached manner.
If he feels a painful feeling, he feels it in a detached manner.
If he feels a neutral feeling, he feels it in a detached manner.

Dhātu Vibhaṅga Sutta