How about installing a temporary hypo injection unit onboard upstream of the seawater coolers? Air bumping (with compressed air) may be more effective than reverse flushing. Agreed, if you could start up the spare seawater pump, the extra velocity together with air bumping may help also.
If you have spare inline plate HXs, then removing one and replacing with a new clean one(which you could purchase quickly off the shelf) is another solution. The work your way through similarly with all the other fouled plate HXs'.
Also check why the trip setting is at 70degC? Can you move it up to say 75degC in the short term till your next planned shutdown? Where is the limitation here?