Greg, what product did Highfield use. Highfield is a good quality dinghy, so I assume, right wrong or indifferent, they used SEADEK. It might be helpful to expand on the description of where the lifting is occurring. If its bubbles in the center of the areas, a glue injection might work, however if it's on the edges, the use of contact cement would work. I have experienced both on the cabin top and sliding hatch cover, where the faux teak was of a cheap variety, held water and got attacked by UV.
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The tan area crumbled leaving only the black layer. Edges and corners also started to lift, even though the product was made with 3M peel and stick backing. In some places the faux teak became waterlogged. It wasn't worth re glueing, it was done after three seasons. My solution was to remove all the fake teak, the glue backing layer and any glue itself. I had to do a lot of scraping, soaking with acetone to remove it all. I replaced the faux teak with a 5mm closed cell embossed gray SEADEK product.
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Work continues, so please excuse the dirty areas. I have some of the cheap faux teak left overs if you wish to have them. PM me if so.