For private BAMS with lower rank around 200k to 800k you can consider these colleges they close late so chance good for you

1.Tilak Ayurved Mahavidyalaya Pune close around 51553 for general but OBC lower, management may take late

2.Ashtang Ayurved Mahavidyalaya Pune close around 67184

3.Ayurved Mahavidyalaya Nashik close around 71888

4.K G Mittal College Mumbai close around 74314

Also Hubli Ayurveda Mysore etc close late but add state variable

https://medicine.careers360.com/articles/private-bams-colleges-in-india-with-neet-rank-40000-to-80000

And if rank worst you can try bigger list upto 800k

1 .Bharati Vidyapeeth Deemed Pune close around 201574

2. Dr DY Patil Pune close around 328076

3. Wardha college close 593954

https://medicine.careers360.com/articles/private-bams-colleges-in-india-accepting-neet-rank-200000-to-800000