I'm not a plumber, but here's what I'd do. I've done this before and have had good success so far with these standards.
Shower will need a 2" drain with an integrated solvent-weld p-trap. Can probably get away with a 1-1/2" vent line for the shower.
Toilet will need a 4" drain line - the water in the toilet is the gas seal, so no P-trap. Use a "long sweep" ell under the toilet to speed the detrius on it's way. 3" vent is OK for the toilet, and you can tee the vent line for the shower into the toilet line to avoid having multiple roof penetrations.
Sink works best with a 2" drain line. P-traps for sinks are under the sink. If proximity is good to the toilet vent, tee the vent line in there too.
Use 4" drain line from the shop to the septic. Tie the sink and shower into the main line with proper reducing DWV T's or WYE's. I like to have the drains enter the pipe on the side, not dump in from the top. Less splash and turbulence that way.
Add a cleanout at the edge of the slab which is a DWV tee in the drain line pointing vertical with a threaded collar and cap at ground level.
Would also be good to add a cleanout under the sink to allow for service without disconnecting the sink p-trap.
I'd plumb it with the sink being the furthest "up-stream". Then the shower, followed by the toilet.
Step 1 - Drain slope to the septic should be 1/8" to 1/4" drop per foot of travel (if I recall). Figure out where you're going to tie into the septic line and how deep the line is at the tie-in point. Measure to the top of the pipe from ground level.
Then measure back to the exit point of the main drain line from the shop. Deduct 1/4" per foot of run from your depth measurement to get the required depth under ground to the top of your main drain line.
Need to allow for ground slope as well, but as you're in Beach City, I doubt there's much. If the ground level where the shop will be built is higher than the ground level at the septic tie-in, you can deduct that elevation difference from your Step 1 value.
The toilet will require the most drop (the minimum distance from the bottom of toilet at floor level to the top of the pipe it connects to) so we'll use that as our base line.
Step 2 - take the # from Step 1 and add the offset required for a 4" long-sweep elbow. The way I visualize this dimension is with the elbow on a table with one of the hubs flat to the table top. Measure up from the table surface to the bottom of the other flange, which is vertical. That's the # you need to add to your pipe elevation number. I don't know what the number is off-hand and Google isn't my friend this morning. Then add another 3" or so for the toilet flange to get your final required height. If that number is less than the planned finish level of the floor in your shop, you're good to go.
If not, you'll either need to elevate the slab, build a platform on the floor of the shop and build the bathroom there, or add a transfer pump that will accept the bathroom drains, macerate the contents and send them on to the septic.
You can also use a backflush toilet and have the drain exit the wall of the shop and drop into the ground from there, but backflush toilets are expensive.
I don't think there's any particular problem with going through the beams.
Hope this helps. Good luck with your new shop - I'm sure you'll enjoy it.
Regards
