Hello (and welcome to the forum),
I saw your post and was interested in the outcome, so, I decided to run the numbers for you for the last week (25th-29th). My assessment uses the TOPS database at regular daily intervals between 05:00 and 23:59. I will also note that a strike day (27th) also fell in the middle of the week so my results are slightly skewed.
Firstly, I have included the 57s and 37s as it provides some overall context;
The following are the TOPS listings for DRS locos (on the books)
On Books Available
37 8 8
57 8 8
66 24 24
68 34 12
88 10 10
As you suggested, I have also included all 24 66s in the XHIM pool in my data despite some regularly used by DB Cargo (their ad-hoc leased to DRS). This does affect the outcome of this class.
Sub'd 66s 5 66031, 66091, 66108, 66122 and 66122 are DB locos
The 57s are used primarily as Avanti West Coast Thunderbirds except for 57306 which is the GWR Sleeper Thunderbird.
THBD 57s 4 57304, 57307-09 are Avanti Thunderbirds at Crewe, Carlisle and Rugby
GWR 57 1 57306 is the GWR Sleeper Spare
As you mention, all the 68s are in their own pools with just 12 actually usable by DRS daily. I have only included the 12 DRS examples in my data.
DRS 68s 12 Split between Crewe Gresty Bridge and Carlisle Kingmoor
CH 68s 6 68010-68015 are in XHCE pool for Chiltern Railways use
TPE 68s 14 68019-68032 are in TPEX pool for regular use
TPE 68s 2 68033 & 68034 are in XHTP pool for ad-hoc use by TPE
The 37s had an average use of 1 per day with a week high of 2 a total fleet utilisation of 7%.
The 57s had an average use of 0 per day with a week high of 1 (+1 GWR Sleeper) a total fleet utilisation of 4%.
The 66s had an average use of 7 per day with a week high of 13 a total fleet utilisation of 29%.
The 68s had an average use of 4 per day with a week high of 6 a total fleet utilisation of 33%. (not including an average of 5 for TPE and 3 for CH)
The 88s had an average use of 5 per day with a week high of 7 a total fleet utilisation of 47%.
The DRS fleet overall appears to be around 30% utilised.
Hope this helps,