Log books don't mean a whole lot... most will never ask or care, some will glance to see what you've done lately. And no one is going to carry a pile of them if they have hundreds of dives, so I'd say, go buy a new log book, try to remember the last half dozen dives or so, and put them in as dive # 144, 145, 146 etc to reflect your actual experience.
Anyone will be able to pick out instantly if you are an experienced diver and not give you any kind of hard time. Heck, today with downloadable computers, a lot of people just have their log experience on a computer - and no one makes them bring in a laptop to show them.
The only time you really need a certain number of dives of a certain type is in instructor stuff... For example, to teach night diving, you are supposed to have done 20 night dives.
As a great example of how important this is.... when I became an instructor back in the 80's, I was 12 dives shy of the Padi requirement... and the instructor examiner looked at my book, then said.. "Uh, you are about 12 dives shy here... You probably just forgot to write some down... so why don't you give me your check, and while I process your paperwork, you can sit down over there and try to remember those 12 dives and write them in... OK?
Maybe that's why I now teach Naui... but either way, no one much cares about seeing all your dives in a log.