You can't just pick and choose dates, and then say the Brewers are fortunate or lucky based off that. A lot of that record since May 5 is driven by the 8 game losing streak in which injuries to key players finally caught up with them amidst the most difficult portion of their schedule. Alternatively, they did get off to the best start in franchise history, and then, post-losing streak with the return of some key injured players and the DFA of Cain, have returned to being among the better teams in baseball. As far as anecdotal evidence, just look at some of the lineups we were forced to put out there in the middle of the losing streak against the Padres and Phillies....
With regard to the offense, it is not this anomaly amongst NL contenders that you keep making it out to be. Even if you don't think it's as good as it's been over the last two weeks, in which it leads the NL in WRC+, its production in that key stat over the course of the entire season places it in a tier with teams such as the Padres, Giants, Phillies, and Braves. Not at the Dodgers, Yankees, Blue Jays level for sure, but enough for a contender such as us with elite arms like Burnes, Woodruff, Hader, Williams, etc.
Furthermore, the team that played in May and June isn't the team that's going to be playing down the stretch in August and September. Besides likely trade upgrades, we're no longer going to be getting league-worst production from a guy such as Cain. McCutchen has already shown that he's not the hitter we saw in May/early June. And guys who were down with injuries for a long period such as Adames and Renfroe should be there as key cogs in the lineup.
This team is right where it needs to be and is backed up by the projection sites, which give them around an 80% probability of making the postseason and a 65% likelihood of winning the division. Not a lock by any means, but in great position.