The Leinstermen's last loss on home turf came against Ulster in March 2013 - and that run has included a narrow play-off semi-final triumph over Gregor Townsend's men last May.
The Warriors' own attempt to get the better of them this season ended in an agonising 28-25 defeat two months ago but Seymour says his side are on the brink of finding a breakthrough victory.
And the wing, who scored a hat-trick of tries against Treviso earlier this month, believes his team can summon up all their past experience to go one step further.
"It has been my best season for Glasgow. I have been with Warriors since 2011, but this season has definitely topped the lot for me," Seymour told the Glasgow Evening Times.
"Obviously we have been very close in the last two play-off semis with Leinster at the RDS, and in particular in last season's semi, we felt that if we had taken it to extra-time we had a real chance to go on and win.
"But what we have to do is put all of that experience to good use this time around.
"We know the environment we are going into, we know the team we are up against very well, so it is not a journey into the unknown and we know that these games with Leinster swing on very small margins.
"We will be going there with a bit of a chip on our shoulder, but we are very much going there with the belief that we can get the win."
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