I would think the 'straight' antenna would work best. Try both but my 'gut' feeling is there is no advantage to the second design.
Without a schematic it isn't possible to tell what the 'linear' output really is but as it appears to be a super-regenerative receiver I would guess it is the data output from the detector and the digital output is the same signal after passing through a data slicer. It is probably (I can't say for certain) representative of the received signal so if you make the data input at the transmitter permanently high so it transmits continuously, you should be able to measure the DC voltage at the linear output with a DVM as a signal strength indicator.
I checked my LCR meter and you are correct, that model doesn't measure below 25pF. There are other simple designs on the internet that can measure below 1pF accurately if you do a search for them, for example: **broken link removed**
Brian.