DP,
Welcome to the forum. We’re happy to have you and it sounds like you have a solid setup and are doing a great job balancing training with the demands of being a new father.
To give you the most useful feedback, I’ll frame this around a few of our core principles regarding programming and long-term progress.
You mentioned progressing by exactly 1kg or 2kg every week, which is a type of “linear progression”. While this works in the beginning, it eventually ignores your daily readiness (what we call autoregulation). On a day when you’ve had 4 hours of sleep because of your daughter, that 168kg deadlift might be an RPE 10, whereas on a well-rested day, it might be an RPE 7.
Instead of forcing a specific weight, we recommend using RPE (Rate of Perceived Exertion) to guide the load. This ensures that the training stress is appropriate for your current state, reducing the risk of burnout or injury.
For progression, we’re looking to get stronger/fitter and then add load, which we discuss in further detail here.
Next, you noted that you rest a maximum of 2 minutes. While this is efficient for shortening your session, it’s on the low end for heavy compound exercises and it may be limiting your strength expression. If you are rushing into a set of 5 while still heavily winded, your performance - and subsequent training load - is being limited by metabolic fatigue rather than your actual muscular strength.
We generally suggest resting as much as needed to perform the next set at the desired weight, proximity to failure, etc. without the rest periods becoming so long that they make the session length incompatible with your life. We often recommend 3 to 5 minutes for heavy compound lifts.
We discuss rest periods, as well as options for shortening your session that preserve training load here.
Regarding your goals, you mentioned aesthetics (hypertrophy) and are only doing sets of 3-5 reps and a relatively small number of exercises. You may benefit from more variety in your rep ranges and exercise selection for both strength and hypertrophy. Adding some higher-rep work (sets of 8–12) and picking different exercises than the big 4 would, and including some unilateral lower body work, isolation work for the arms, shoulders, and legs could be useful.
Here are two free resources that explain the logic behind our changes: