Why do measurements displayed in multimeter inconsistently vary by factors of 1000 depending on range?
The relevant part in the manual is


200 Ohm range can show  000.0 - 199.9 Ohms
2K Ohm range can show   0000 - 1999 Ohms
20K Ohm range can show  00.00 - 19.99K Ohms
200K Ohm range can show 000.0 - 199.9K Ohms
20M Ohm range can show  00.00 - 19.99M Ohms  

Regarding your results, they should be interpreted as:

2000 ohms: 1025-1030 Ohm
20k ohms: 01.02K - 01.03K Ohm
200k ohms: 001.0K Ohm
20M ohms: 00.00M Ohm