First state your specs !!
This may mean your question is irrelevant.
If you have a GPS, you can always get the message of real time.
So do you want to null frequency error or get accurate time? Then what tolerances for either?
If you only need an accurate clock frequency, you can buy these cheaply instead of using a crystal. (X) It will be temperature compensated and thus called a TCXO crystal oscillator chip and costs ~>$1, depending on Qty and [ppb or ppm] frequency error and temp. range.
SER4045CT-ND is Digikey's part number for a 10pF 40MHz Xtal from Epson
Therefore change your load caps from 100pF to 15~20pF to increase to nominal f C1+C2+ Stray+C input= load pF to include stray input.
Same for 38kHz Xtal is 9pF, therefore, 18pF on out and 15~18pf on input.
If you want an accurate frequency this is done with time interval counts best with high resolution as the counts must exceed your desired error in ppm. Again the time interval of this error averaging must be defined in your SPEC.
If the frequency error is less than your resolution, you cannot read any error. So to force this without having to use 32-bit counters, you can inject a sine wave lookup table of offsets to exceed your resolution and accumulate your error. Or it could be a binary offset of phase incrementing +/-x,+/2x,+/-4x etc. Any source of noise is possible as long, as there is 0 average phase error or latency added.
Digital clock phase or frequency error correction must be applied to the frequency at or above where you want stable by mixing at or above that frequency. If you mix at a lower frequency then time integration error correction is needed by accumulating error.
If you want to correct using PLL design then one uses a Vr controlled diode instead of one cap to reverse bias to modulate pF with DAC voltage from high series R-value.
Usually, the synchronized clock is inverted to the measured clock to allow a value to vary from the 50% of T=1/5 by the variation of the injected dither. This could be a sine quantized by any number of levels and determines how quickly you need to achieve your ppm or ppb error measurement.
When I designed a PLL clock with 1e-12 stability for Doppler tracking, I used VLF signals since GPS was not invented yet and reduced the clocks to the lowest common frequency of 100Hz from multiple global radiated RF land sources. This enabled me to eliminate frequency error and measure phase shift from a moving receiver.
Then 20 years later in the 90's, I contributed to the design of a 1ppm TCXO for < $1 using my special 3rd order equations to correct AT- Xtal temperature error curves using a thermistor and tested varicaps binned for V/pF ratios and Xtals(crystals) tested at 24'C and 70'C in 10 seconds for the VCXO to tune 1GHz radios within 1ppm. It was just one tooth in a giant telemetry 2-way AMR network design we designed for 1 million clients sharing 6kHz ISM BW for automated meter reading.