From a pure cash stand point I do not think the math will work out well versus a value. I'll give a back on the envelope math example (I am assuming the rack rates on value rooms will go up the same as time value of money for the
DVC purchase and dues will increase about 3.5% per year) If you take the time value of money out of it then the math works better for DVC. If you were to fiance the DVC purchase then the math really changes to favor value rooms.
7 nights at saratoga springs studio in choice season (2nd lowest time of the year) =104 points. Resale at SSR is $85 a point.
Purchase cost is $8840. Yearly fees = $5.43 per point =$564 per year (every year till the contract ends and they will go up every year)
7 Nights at All stars for Oct 1-8 (7 nights)=$951 including tax
Being super simple about it this math would take you 70 years to break even since the dues increase in price over time.
You could also look at it without putting into account time value of money. If you do this and assume dues will increase at the same rate that the rack room rate will increase your math works out better. Breakeven will be closer to 20 years.
You could just not look at anything increasing at all and be super simple (also incorrect) and say that the rack rate is $951 a week, dues are $564 a year so my "savings" is $387 a year. $8840/$357 = 22.3 years for breakeven.
Any way on a cash level DVC cannot compare to a value even on a resale level. That being said we love our DVC and we take a lot of vacations with our family and friends now in 2 bed rooms that we never would have done if we were paying cash price for the rooms. The value for DVC is much better when you compare it to deluxe villas that run $1000 a night.
I like your idea about renting for one trip. If you can rent 7 nights at saratoga as an example that cost would be about $1350 or so depending on the rental rate per point. You can then see if the DVC setup feels like it is worth it to you over the value rooms. If you don't think it was worth it then you are only really out the $400 difference or so between a value room and the rental cost as opposed to owing a $9000 timeshare.