One winter afternoon in Pasadena, a group sat outdoors on a hotel/restaurant patio that was warmed by some very vertical pyramid-shaped heaters that were really attractive and seemed quite effective. The closest example I can find is in the link below. It came to mind because of your space limitations.

Here is a link that might be useful: Vertical patio heater

I wonder if fire pit tables are effective for heat?
It would allow me to have one thing that could be left out all year long (assuming it it is fully sun, rain and rust proof) and do double duty as a year round table.

I just rearranged some of the pants. Here is another picture showing the ground space available.

I read some reviews that said the pyramid shaped heaters give a really nice-looking light show at night, but are poor at providing useful heat.
Maybe it depends on the specific model of heater and maybe the the people complaining had a larger area to heat than I do.
However, even though my patio is so small, it is still wide open and uncovered, so there is nothing to contain the heat and I would probably need to situate the heater quite close to where I would be sitting unless it really "throws" out a lot of heat without a fan assist.

Another option I thought of would be a table top heater. I would need to get a table larger than a bistro set to accommodate it or else there would be not be enough space to even set down a tray or laptop with the heater on top.
I could also set it on the floor or on a low side table next to the chaise lounge I get and it would be small and light enough that I could easily pick it up and store it inside when not needed.
Anyone try those table top heaters or else the pyramid heaters described earlier?.
The ones by Lava Heat Italia look good, but pricey. They do have a tabletop version that's only $150 at Costco though.

See the link below the photo.

Here is a link that might be useful: Lava Heat Italia

I like the easy movability of these heat lamps.
They even look good when not in use.
easy to move around, lots of heat.

I like the look of that heater. How close to it can you put lawn furniture, and does it make much noise?

Can a propane BBQ do double duty as a heater so I don't need 2 objects?

How close to it can you put lawn furniture, - pretty close but use reasonable caution.
and does it make much noise? - no.

Can a propane BBQ do double duty as a heater so I don't need 2 objects? - never tried it - doesn't sound too attractive though.

You might like the smaller table top heaters (miniature versions of the traditional stand type) or perhaps one of the propane operated coffee tables. - no a lot of heat - more ambiance than warmth.

I decided to get a patio heater in a different style. I like the looks of it and the fact that it came 95% pre assembled in the box.
The only disappointment is that, if it is that you really need to be right on top of it (within 1 ft away) for it to feel warm since 90% of the heat just goes away into the sky in an open uncovered patio.
I'm thinking that I may eventually get a small covered gazebo just large enough to hold a bistro set.plus the heater so I can sit outside on colder days and not lose 99% of the heat output from the heater.
Otherwise, I find this heater mostly decorative. It adds nice atmosphere on nights when it is not cold outside.
I have to sit so close to it that my shoulders are almost touching it to get real heating benefit.