Would Upton's technique have produced better results on day 3?

If they tried stacking the brigades in an assault against Cemetery Ridge the repulse would have been even worse. The masses of troops would have made the artillery fire even more devastating. At Spotsylvania it partly succeeded because; they attacked at first light, Lee had ordered artillery back because he thought Grant was moving his army, and the distance the attackers had to go was shorter than what the Confederates had to do at Gettysburg. (I'm talking about the second attempt and I don't know the distance between the lines but it was definitely shorter than the mile that Pickett had to cover)

At Spotsylvania the Confederates had fewer troops to cover a longer defensive line than the compact line with more troops the Union had at Gettysburg. The only salient the Confederates could have attacked at Gettysburg was Cemetery Hill, but they would have had to get the troops organized in the town. I'm not sure how/if they could have done that effectively, it would be a good question to ask a real expert on the battle.

The echelon attack on the second was a mistake because they got started too late in the day. It took too long with the daylight they had left. One massive simultaneous attack would have been better regardless of how they organized it.

Interesting counterfactual discussion, and it certainly represents a better option for Lee than what he actually did. However... and this is totally personal opinion... I think it would still have failed. I think a column arrayed in an Emory Upton-style fist and aimed right for the copse of trees would have had more initial success than the Pickett's charge we know. Remember, Armistead and a few hundred of his men DID reach and briefly break the Union center even when attacking as part of a long line. A solid column aimed at the same spot surely would have broken through. I just think they'd still have sustained heavy casualties and would be completely disorganized (and perhaps demoralized too) by the time they reached Union lines. At Spotsylvania, this disorganization is what eventually doomed Upton's attack even after smashing a seemingly impenetrable Confederate position. Union troops were not quite sure what to do with their success, and Lee was quick to organize and mount a counterattack. On the Union side at Gettysburg, unlike on the Confederate side at Spotsylvania, fresh reserve forces were already close at hand waiting for their chance. They didn't need a Robert E. Lee to pull together a miraculous counterstrike. They just needed Confederate troops to appear so they could rush in and kill them. Bottom line, I think a massed column attack WOULD have smashed through the Union center, and, for a few minutes, it may well have appeared to all involved that Lee was winning the battle and, perhaps, even the war... but that would have been a mirage. I think the shoulders on either side of the breech would have held and Union reserves behind the center of the line would have quickly pitched in to the attackers. Finally, I think after marching across a mile of open field with shot and shell pummeling them the whole way, the Confederate force would have been at or near its physical limits by the time they reached the Union line and wouldn't have sufficient order to respond as nimbly as required. Fresh enemy troops on their front and flanks and no hope for any further support or reinforcement of their own would have eventually spelled defeat for the Confederacy. In the end, I think the only difference would have been where the majority of Confederate casualties happened... it would have been within Union lines rather than in front of them.

Having said that, I am very curious to hear how your attack went in the boardgame.