This is such a loaded question, because no matter how many times you go, or how many days you have, you will not have enough time to see it all.
Here is what I consider to be some of my favorite days back-to-back on a River Trip:
Spend your time at Tapeats Creek & Deer Creek (whether you do the loop hike over, or just hike to the patio), then move down and camp. Next day, go down to Olo, and if you have some strongish climbers they can get up into Olo and haul the less-experienced/willing up the mouth. You can easily climb up the next couple of raps and get into the Muav narrows. Then just rap back out. If this is not your style, then stop by Matkat, do the hike up, run Upset and camp around Ledges to set up for your Havasu Day.
Next day, do the Havasu thing, then move down to somewhere above Tuckup. YMMV depending on how much time you spend in Havasu.
This next day is one of my favorite ways to spend a day in GC and get so much bang for so little effort. Stop at Tuckup in the morning. There is a great hike here up past the narrows. Spend a few hours. Go down to National and do this hike up to the barrier chock. Have lunch either before or after the hike. National is such a nice canyon. Move down to Fern Glen and do the hike up to the waterfall. Either camp at Fern or move to something like Mohawk. A day spent in the Muav at Tuckup, National and Fern is incredible, it is highly recommended and highly memorable! It is also a great way to spend the day before Lava.
The past few years we have also done the full descent of Silver Grotto by leaving half the boats at Shinumo Wash (29 Mile), taking the other half down to the beach opposite Fence Fault (River Left above the riffle), heading the Redwall then hiking back up to the top of the Redwall in Silver Grotto. This is about a half day adventure and can get you into a nice little pocket away from several of the other trips that launched with you, and the motors who launched a day behind you (mid Sept. Launch may still be a few motors on the River I believe).
The camp at Saddle Canyon on the downstream sandbar has good early shade. Also a nice hike if you haven't done it.
The adventurous may like a layover at Enfilade camp with an ascent of the Enfilade Route up to the top of the Redwall or into the Supai. Here is one description of that. Note there is some exposure:
Grand Canyon Hiking: Enfilade Point Route
Back in the Bass area you could spend a layover and get up Shinumo Creek a good ways towards Modred Abyss. This would be a LONG hiking day, maybe even worth pulling a backcountry permit and doing an overnight up there?
Otherwise, be creative, see some new things. Make the obligatory stops at the attractions, but consider laying over at new spots and doing new hikes. With only 18 days, layovers will be tough, but doable.
Have a great trip!