Again, we need to know more about your specific lifts, specific goals. Are you working mostly on a squat? Or are you working on your C & J? Or deadlift? Or what??
Do strength training when you feel freshest and most energized on average. I hate mornings, so if I train in the morning it is light, and evening is heavy. Some people are the opposite.
For your purposes olympic lifts with strength training is probably best. I don't know what the template they used on the website is since I don't have a subscription there, but if your goal is strength then 1) train strength when you feel best in the day and 2) keep your conditioning separate from strength sessions. So no, don't do wheelbarrows, farmer's walks or sled pulls with strength training. If you do them do them in the morning.
Dude, honestly you do not need to do that if you're doing WODs in the mornings.
Crossfit people always get worried about not doing enough conditioning shit. It drives me nuts. I train a chick who is a crossfit coach in the olympic lifts 5 days a week. Our strength sessions last on average 2 hours. We do absolutely no conditioning work at all because she does the WODs 3 days a week on average. She's doing just fine without conditioning. DO NOT add extra conditioning.
WODs 3 days a week, no other conditioning. At all. Unless you like to jog to work some soreness out or something, that is not conditioning that is "loosening up". Not my thing but some people (notably fighters I've worked with) like it.
A general guideline would be total time spent on WODs and conditioning are not to exceed 30 minutes x 3 days a week (i.e. 1.5 hours in a week). This does not include warm-ups obviously.
You can peak conditioning in 6-8 weeks max. Strength takes years to build.