There is! Long story short, Select-Object is doing the truncating here. Here's one way to get the first untruncated line in a Select-String output
$(Select-String -Path $logDir -Pattern "SRVE0242I:")[0].Line
When you run into something like this, you can break down the individual steps to determine what's happening by piping things to Get-Member. Here's what's happening in the code above:
Select-String <# args #> | Get-Member
Select-String gives us a MatchInfo object, which (as you've correctly determined) has a 'Line' property. When run on it's own, Select-String will actually spit out all the information you're looking for, and will not truncate it by default (at least, on v6.0.0-beta). It does give you an array of MatchInfo objects if it finds multiple matches, so you have to index into that array if you just want the first one (like I did above).
Select-String <# args #> | Select-Object Line | Get-Member
Select-Object applies PowerShell's default formatting for objects which, in most cases, will truncate your output for easier viewing. For objects with a bunch of members (like a MatchInfo object), it will try to do one per line by default.
Select-String <# args #> | Select-Object Line | Out-String | Get-Member
Out-String directly translates it's input to a string. That is, rather than trying to cast something to a string or pull a string Property out of an object that's passed to it, it just changes whatever it receives into an object. In this case, it turns the already-formatted MatchInfo output into a string. Nothing happens to the output on the terminal, but Get-Member will reveal a String rather than a MatchInfo object.
It's not directly relevant here, but if you're interested in modifying the default formatting, it's governed by the types.ps1xml file.