To crunch the filesize for schematics, you need to reduce the colour depth to 16 (4 bit) and save as PNG.
Irfanview saves a 3261x2059 greyscale 4bpp PNG of the schematic copied from your PDF with a filesize under 250K
You'll need level shifters between the 3.3V MAX31855 Thermocouple interface and the 5V ATmega328P. Don't forget to make the MISO one tristatable, controlled by the MAX31855 /CS so it doesn't conflict with the display. Check whether the display uses 5V logic levels - Raspberry PIs use 3.3V levels so your direct connection to the ATmega328P is suspicious.
It would probably be worth adding additional SSR control outputs so you can support control of an oven fan for more even temperatures during rampup and soak and extra boost elements for faster peak reflow.
Consider supporting multiple thermocouples with additional MAX31855 chips for better temperature control. There's no need to populate all the MAX31855 and Type K connector footprints until you need them, but I'd put four footprints on the board with a 74HC138 3 to 8 line decoder to drive the /CS pins from only three I/Os to select the SPI device to access + master /CS to a '138 enable pin.
Also add a header with all the spare ATmega I/Os on it, the SPI bus, all spare '138 /CS outputs, 5V, raw DC in, and Ground for future expansion.