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What is the typical conversion efficiency during a normal single-rest mash (152 F/67 C, 3 l/kg)? I usually get around 80 %, but Braukaiser claims that it should be close to 100 %. I mash for 60 minutes.

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I don't think there is a typical conversion efficiency for homebrewers since it very much depends upon the nature of the equipment. Mash tun shape/depth and use of recirculation will have a big impact. If you pushed me for a figure, I'd say anywhere from 80-98% is typical for mash conversion efficiency.

I measure the SG of the wort continually throughout the mash, and find that often conversion is still ongoing after 90 minutes (my usual mash time) since the SG of the wort is still increasing.

Stirring the mash, recirculating, using a sufficiently fine crush, appropriate water to grist ratio, optimum pH, and giving enough time should help you reach close to 100% mash conversion.

Of course, your actual extract will be less since there are losses during lautering and sparging, but getting the mash close to 100% conversion efficiency is much easier than improving lautering or sparge efficiency, since it typically doesn't involve changes to the equipment.

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