Here is a 'pork chop plot' of missions to 'Oumuamua using a Jupiter powered gravitational assist (or a Jupiter Oberth Manoeuvre, JOM). Refer to the Figure (1).
Essentially, what we have are three coordinates where firstly the horizontal axis shows the launch date, the vertical axis shows the flight duration, and for every combination of these two values we have a colour, indicating the ∆V, as you know determines how much rocket fuel would be needed to get to 'Oumuamua. We naturally want this to be as low as possible, and therefore the colours to be as deep blue as possible, for a mission to be feasible.
However when we encounter Jupiter, we also want the perijove altitude (the closest approach to Jupiter) to be positive (to avoid a collision). This cuts out most of the landscape of the first figure and gives huge blank regions in the second figure (Figure (2)) of clear infeasibility.
In fact we only have a few spikes in low ∆V around 2030 and 2031, other than this, there are absolutely NO VIABLE MISSIONS to 'Oumuamua before around 2040, and after 2026. You now see the EXTREME IMPORTANCE of making sure we realise a mission to 'Oumuamua by the years 2030/2031, if we are going to use this route to achieve an intercept and transmit data back to Earth.