There are many things that I don't understand.
This is not a tight loop and you don't know if the data was available:
Wire.requestFrom(0x4C, 1); //set up read
byte regVal = Wire.read(); //read
I don't understand what seems wrong to you and I don't know what you mean with a very tight loop.
I don't know if you have removed the Wire.endTransmission() after the Wire.requestFrom().
You may not connect the Uno SDA and SCL to the TMP112. It might work if you carefully calculate the voltages with the pullup resistors, but then it will probably not be within the specifications in the datasheets (for both the Atmega328P and the TMP112).
Do you use the bare chips for the MAX14622 and the TMP112 ? So there are no modules with extra components ?
The Arduino Uno is a 5V board. When using a level shifter you must power the "HV" with 5V, or else the level shifter shifts the signals up to 3.3V which is not much use to the Arduino Uno because it needs 5V signals.
Without level shifter (which is wrong anyway) there are no pullup resistors.
Sparkfun level shifter: https://www.sparkfun.com/products/12009.
It has 10k pullup resistors on both the high side and the low side. That is enough pullup for most situations.
Is there a reason to use the MAX14622 with 1.8V. It will work with 5V as well. You can connect it to the Arduino Uno without level shifter and power it with 5V.
When you use a level shifter for something else, then you should still connect the MAX14622 directly to the Uno (not via the level shifter).
Powering the MAX14622 with 3.3V is not okay, because the SDA and SCL for the Uno board use 5V levels, it is a 5V I2C bus.
Powering the TMP112 with 3.3V is okay, but the SDA and SCL need the level shifters.
Can you show your new sketch and new schematic ? There are too many things that are not okay.