Dear Jamie Douse,
from the Block System Training methodology point of view, your strength training program should have the following periods:
A1 - The preparatory stage. Strengthening of: most important muscles for the speed running, their antagonist muscles and upper body muscles; with the use of 10-5 RM method.
A2 - The maximal strength stage. Increasing of maximal strength of pushing up leg muscles, with the use of 1-3 RM method.
A3 - The speed-strength stage. Increasing of explosive strength and maximal anaerobic power with the use of the complex super-method, in which the first work (tonic) consist in 2 sets of 6-8 jumps with Russian Kettlebell held between the legs and the second work (developing) consist in 2 sets of 5-6 repetitions of multiple long jumps (6 or 8 jumping passes from leg to leg).
B1 - The specific power stage. Increasing of the running footsteps length and the anaerobic alactacid capacity (of the alactacid threshold ) with the use of the alternate leaps in slope.
B2 - The specific running speed stage. Track & Field Training: the performing of the 200 and 400 meters runners specific training methods (including glicolitic interval training).
Block C: 400 m e 200 mt distance running in preliminary competitions.
Your questions concern the strength exercises contents of the Block A (A1 and A2).
To understand well my following comments it will be better see the general scheme of the training programs stages constructions in my book "Special Strength training: a practical manual for coaches": Program for High Level Tennis Players (page 113), Special Strength Training Program For Basketball Players (page 104).
Stage A1 main exercises.
1. Strengthening of the most important speed running muscles groups (involved in push up and long footstep), for example:
- Barbell squat (10-5 RM)
- Heel (cal raise) with bar on shoulders (10-5 RM)
- “Soleum”- heel (cal rise) with weight on the knees (10 RM)
- “Long” jump exercises are executed on soft, resilient ground (page 42).
- Jumping exercises with overload: Squat jump with barbell and Scissor-lunge jumps
(jump out of a lunge [stride] position with a switch in the legs, alternating on every jump on the page 44, figure 30 and see also the Program for Top Level Middle Distance Runners on the page 88)
- Exercises for the hip flexor muscles (for example, figure 31 on the page 44 or figures 6a, 7 and 8 on the page 7)
- Long footstep walking with barbell on scolders
- Low Scissor-lunge jumps with barbell on shoulders (the energise switches in the legs)
If you want, at this stage you could include other strength exercises (that you normally use) and also Deadlifting, but I think that for runners, Squat is more important than Deadlifting.
2. Strengthening of upper body (arms, back, abdominal) and legs “antagonist” muscles with standard block machine and free weight exercises (10 RM method) with large movements amplitude (not with the Bodybuilding technique).
Stage A2 main exercises.
Increasing of leg muscles maximal strength (for the push up power increasing):
- Barbell squat (3-1 RM)
- Heel (cal raise) with bar on shoulders (3-1 RM).
You can also continue the hip flexor muscles exercises use, but not so match.
The barbell exercises technique should be standard for Olympic sport disciplines.
The level of the maximal strength can be increase still you “should be able to squat 1.5 times bodyweight” (I think that your “theory” is right, but, anyway, it’s a very individual question).