Are you sure that the design that worked didn't use 1k resistors and not 10k?

For 350mA out, you should make sure you manage 3.5V in.
At 3.5V in, you should make sure that you are able to source about 1.1mA.
But to get a voltage loss of no more than 1.5V at 1.1mA, you would need a pull-up of 1.5/1.1 [k] = 1.3k.

And remember that when the ULN doesn't open fully, then you will get a lot of power loss in the transistor, so the ULN will get hot. In your case, you should make sure that it is either fully on or fully off.

By the way - have you considered the voltage loss in the ULN when computing your 3V for the laser? Vce(sat) at 350mA is typically 1.3V and max 1.6V. 5V - 1.6V - 2*0.7V could give 2.0V to the laser. 5 - 1.3 - 2*0.6 could give 2.5V.

Is this what you are doing with your other circuit too? Using an ULN to drive 250-350mA to a 3V laser in series with two diodes? How close do you get to the intended voltage and current?

Edit: Just remember also the maximum allowed current when holding the the outputs low - for one pin, total for the port and total for the chip. Too strong pull-up will overload the port/chip.