I would go one step further and suggest maybe using actual events as your 5x5 lifts. Maybe a log or axle press, stones and tire. Your push press will hit your pressing, Stones will hit a rowing and front squatting motion and tires (depending on your style and the weight of the tire) will be anything from a pull from the floor to a power clean. Throw in some light weight but long distance farmers or sled dragging on your off days as a recovery/GPP exercise (I would suggest even using straps on your farmers after maybe one set to grip failure just to prolong your walks, which will increase your core stability and conditioning).
Frankly, I have found that any work outside of pure event work (contest conditions or max efforts once a week) is all support work, and as such it doesn’t REALLY matter what you do since it is all just general carry over stuff. Focus on your weaknesses during the week and drill the event technique work.
Just like a WSBB program, your supporting work should address YOUR weaknesses, and should not be some cookie cutter template. If you aren’t sure where your weaknesses are, get someone in a training group to tell you where you could improve. Maybe you have a weak log clean, or maybe you are very wobbly after you lock out. You can address those things in gym training (pull troughs for log cleans can help get a feel for driving the hips to move the log, maybe just doing some timed handstands against a wall will help your shoulder girdle stability in a lockout). Addressing weaknesses is rarely about hitting lifts in a typical way.
Just something else to consider. At the end of the day you have to make progress, and how you go about that is irrelevant. You will find as many different training philosophies in strongman as you will find competitors. Even in my training group, with roughly 10 regulars, no two people do the same work through the week. We trade notes, talk about what has worked for us, etc. But the only common training we all have is the work we do on Saturday event days.
ThreeWhiteLights: You post at Marunde Muscle at all?