Chain, tensioner, and guides are not a huge expense if you DIY, and they will increase your confidence in the engine. Have you popped the valve cover to check out the cam? I just had mine off the other day (same car - 85 380SE) to replace the oiler tube connectors and the valve cover gasket. Removing the valve cover takes all of 5 minutes.

As for the gas mileage, are you sure you are getting 19 to 23 around town? That seems nearly impossible. I am very militant about keeping records. I have a spreadsheet which, among other things, contains entries for every gas station fillup, including odometer readings, trip readings, number of gallons put in, grade, price per gallon, etc. On my 85 380SE which is in awesome mechanical condition, I average 16 mpg around town and 19 on the highway. There is almost nothing I can do around town to change that 16 mpg around town figure. If I turn on the A/C and drive like a maniac, I still get 16 mpg. Same thing if I turn the A/C off and drive like a granny - I still get 16 mpg, most likely due to the low end torque nature of a V8. I even have the original window sticker which gives EPA estimates of 16 city / 19 highway. And we all know how incredibly optimistic those EPA estimates are.

My 300E, which is pretty efficient, will never see 23 around town, and it is lighter and has more horsepower.

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08 W251 R350
97 W210 E320
91 W124 300E
86 W126 560SEL
85 W126 380SE Silver
85 W126 380SE Cranberry
79 W123 250
78 W123 280E
75 W114 280