Drip water system low pressure
The problem is that pressure loss in 1/4" tubing is relatively high. You'll have much better results if you use larger tube for distribution and use the 1/4" only for branching to single emitters (maybe two, but likely not more than that).

Pressure loss in a tube is a function of flow (gallons per minute, or other similar unit) and tube diameter. As tube gets smaller or flow gets larger the pressure drop increases. This happens remarkably quickly with 1/4" tube.

I suggest building your system by working from the most distant emitter back toward the source. Pick an emitter and measure off the length of tube needed to get to where you want the next fitting to be. Instead of connecting to that fitting, connect to the water source. Verify the flow from the emitter is satisfactory - this confirms that the 1/4" tube is adequate for the flow that lone emitter requires. Add the next emitter, tube, and tee, and test with the water source again. After a few iterations you'll have an idea how many emitters a length of 1/4" tube can supply. It's at this point that the system needs to transition to a larger tube.

Since the system is already assembled, you could repeatedly break it down into smaller pieces until it becomes a set of subsystems that each work well on their own. These would then be joined to a larger distribution tube from the water source.