* Does not having an auto-pilot limit the usefulness of an Instrument Rating?
No.
* How much does not having an auto-pilot impede safety?
Only to the extent that it'll increase your rate of fatigue while you're in IMC. It's a lot easier to monitor what an autopilot is doing than to fly. However, with that much more hands-on time, you should remain better at instrument flying than if you had an autopilot. Be cognizant of the fatigue issue, and it's a wash.
* Does not having an auto-pilot limit the usefulness of the Instrument Rating enough to not get the rating?
Absolutely not! If you plan to travel, you should plan to have an instrument rating. It really helps the dispatch rate. I've had flights where I literally was IMC for *seconds* but couldn't have made it VFR (Solid OVC008 at departure with a deck that was maybe 200 feet thick, clear at destination).
* How difficult would it be to remain proficient and current when I'm only flying 5-10 hours a month max?
That depends on what the 5-10 hours are. One leg with one approach ain't gonna cut it.
I do have Zulu's; prop balance is on my list, but haven't gotten around to it. Mostly it's mental exhaustion probably because I want my wife (and now baby) to have a good trip, so I'm sort of OCD about having everything go according to plan and have everyone be as comfortable as possible (just my personality trait I guess). I know they count on me to make our trips as safe as possible, and to make the right decisions and I take that responsibility very seriously.
If you're bushed after 2 hours... You worry too much, and your worry is going to decrease your safety. I also want my pax (usually my wife) to have a good trip, but your "everything go according to plan" is a red flag to me: In all GA flying, you need to be flexible. GA is always an adventure, it's just not always the adventure you had planned.
Your pax need to understand that you are going to keep them safe, first and foremost. If that means you don't get home tonight, so be it - Better than not getting home at all! If there's a NEED to be home tonight - Best leave early enough that you can land somewhere and rent a car to finish the trip if need be.
I'm very lucky to have a wife who not only loves to travel via GA, she understands that need for flexibility - Last weekend we went on a trip where there was a chance of icing on the latter half. I told her "We may fly to within 5 miles of our destination and have to turn around and come home" and she was OK with that.
If your wife is inflexible about such things, buy her an airline ticket. If she understands the need for safety over operational "requirements" you should be good.
If YOU are inflexible - You need to learn to be flexible with your plans or stop thinking of GA as a method of travel. The instrument rating is completely irrelevant to this.
In 1200 hours of flying and nearly 900 hours of cross country, that is my biggest takeaway: You MUST be flexible in your plans. If you are really obsessive about doing what you planned or if you're not good at making new plans on the fly, then you need to make lots of alternate plans in advance.
Here's a few examples of things that have caused me to alter plans:
* Worst delay (2 days) was caused by a muddy runway. Weather was VFR. Had to wait for it to dry out.
* On the way home on a day trip ahead of a storm, I had the field in sight when Approach said "Winds now 270 at 19 gusting 47, say intentions." I diverted to a field farther ahead of the storm, walked to dinner from there, flew home after dinner (and after the storm had passed).
* I've been in a plane, engine running (even taxied out once) when approaching storms just got closer than I was comfortable with faster than expected. Shut down, try another day.
* Widely scattered t-storms, including a cell over the destination for a $100 burger run (06C). That one cell did not move - Got nearby, it was still there. Flew down the lakeshore sightseeing, came back around the south side, still there. Was watching it on ADS-B the whole way. Finally just kept flying, all the way home, had my $100 burger at the restaurant next to my home field.
Note that none of the above had anything to do with being instrument rated - The IR would not have allowed me to finish the planned flight in any of those cases! But, here's a few situations where the IR was a real help:
* Heading home from SBN VFR one night, started snowing... Then started snowing harder. Altered course to remain VFR, air-filed IFR, flew home, shot the ILS to about 800 feet.
* The aforementioned 200-foot deck a few hundred feet off the ground on an otherwise beautiful day - And this is a frequent theme! Low-ish clouds with low-ish tops, beautiful sunny weather on top.
There have been others, but you get the idea.
IMO: Finish your instrument rating, and you'll be glad you did. Make sure you and your pax are flexible with plans. Take a deep breath and don't overthink things lest you wear yourself out!