In your hypo, Murray is born on August 17, 1970 (Courier's birthdate). So, let's map those tournaments w/ Murray's results in his original timeline:
AO 91 (2007: 4th round loss), 92 (2008: 1st round loss), 93 (2009: 4th round loss), 95 (2011: finals loss), 96 (2012: finals loss)
RG 91/92 (2007: DNP/2008: 3rd round loss), 96 (2012: 4th round loss)
Wimbledon: 90 (2006: 1st round loss), 91 (2007: DNP), 92 (2008: QF loss), 96 (2012: finals loss)
USO: 91 (2006: 4th round loss), 93 (2008: finals loss), 94 (2009: 4th round loss)
I see 4 shots at a Major under this timeline (bolded). At the 1993 U.S. Open, he has to beat peak Sampras. At the 1995 Australian Open, he has to beat Agassi and Sampras. At the 1996 Australian Open, he has to beat Becker, Chang, and maybe Agassi. At Wimbledon 1996, he has to beat redlining Krajicek. So, basically, he has a good shot at the two 1996 Majors, a longer shot at the 1993 U.S. Open, and a much longer shot at the 1995 Australian Open. So, he probably ends w/1-4 Majors, pretty similar to his actual haul.