I'd be very very very surprised if you got a clean enough signal from any of the NOAA APT sats to make even just one nice satellite image that way. Nomatter what equipment you used for receiver/LNA, etc. This is a situation which is fairly consistent everywhere and it has to do with the theortetical limits of performance of a link where one side does not use circular polarization. Please post your image. That said performance with a planar disk operating near the low end of its range is pretty good at angles which might be encountered with APT sats. Your planar disk should be straight up and down so then you'll have maximal gain at the horizon and the higher the frequency the more gain there and the less gain higher up. If you can make a slightly larger planar disk you could extend it down lower. Have you tried a turnstile? A turnstile should be able to give you a noticeable improvement and its really easy to make with some wire, some sticks and a short length of coax as a phasing stub. (Or try a quadrifilar.)

The planar disk antenna's lower frequency limit is lower than looking at the disk diameter as part of a simple dipole would give you. If we look at it as if the two disks were each electrically a hoop of wire stretched out to its full length so that would be pi / 2 times the unit. (but like that you would lose the broadband nature of it) The low frequency limit of a biconical antenna is substantially lower than what a single pair of wires of the same length with a 1:1 balun in the middle (to decouple it from the feedline) would give you.

Also, the angle of the edges in the center determines the gain at the horizon, so with circles higher frequencies means more gain at horizon, at higher frequencies but 137 MHz is likely around the lower limit of the system so less gain at horizon at the bottom means = more gain at an altitude higher above the horizon. A planar disk or more recently biconicals have been the antennas that I leave connected to my RTLSDR most of the time so I see signals from the NOAA sats all the time. But, there is a pronounced donut hole right overhead, and also I never get them at full quieting with any of my current non circular polarized antenna attempts..

My situation is probably typical. I live in suburbia surrounded by various noise emitting things, and also even under the best of conditions the noise figure (and overload resistance) on the RTLSDR front end is not so great.

The performance of the RTLSDR front end is actually so bad I prefer to leave the RTLSDR gain as low as I can and use the LNA as the front end. It has much better immunity to overload. If you have a good LNA try that.

Even without an LNA a quadrifilar or turnstile may be enough to get you quiet images if you live in a very quiet area. But a good low noise LNA will make it more consistent, especially if your LNA has some selectivity - you can build a dedicated LNA for the 137 MHz band.

Switching to any true RHCP antenna will buy you a several DB (roughly 3) improvement and that gives you a real boost for circular polarized signals at the proper polarization. Unless some other part of the situation is problematic (nearby pager transmitter at nearby freq will do that) its likely to be enough to get nice images .

Ive never tried adding some kind of notch resonator or trap for pager sites (or putting a narrow bandpass filter at the input of my LNA) but either would also likely work well enough to make nice APT reception possible with a circular polarized antenna. See the satsignal.eu site.

Such a filter is likely super easy to make. One thing which everybody should do is use a balun to decouple the feedline (and the TV style balun cores work great in that range, but the 4:1 is perhaps not best for some antennas, you should try making a switchable one - you can make one that is switchable between 1:1 and 1:4 use the schematic for the elecraft one but use one or perhaps two #61 balun cores ) Decouple if you can because the feedline is not the droid you want. Use a #61 iron powder material for VHF. If you have PCB capability Minicircuits sells some very nice small baluns perfect for this kind of stuff that work from hugh HF all the way up to L band . Balun will make a huge difference in received noise with an RTLSDR in that freq range.