The dictionary yielded 103 pairs, but all of them contrasted the schwa not with the /ɪə/ diphthong but with two vowels /ɪ/ and /ə/ forming two syllables. This distinction can cause mishearings, but they are not associated with any particular group of learners.
Meanwhile Peter Berry has suggested the pair gluer (machine for gluing) versus glue-ear (a medical condition), which is closer to true minimal pair, though there might also be a stress difference.
The density figure is irrelevant.
Alexandra Alexandria aural oriel Beryl burial beryls burials boarder bawdier boner bonier boozer boozier bumper bumpier Carron carrion catcher catchier cedar seedier chatter chattier choler collier cholers colliers chopper choppier clamour clammier cocker cockier corner cornier corners corneas creeper creepier curler curlier dreamer dreamier dresser dressier dumper dumpier duster dustier falter faultier fatter fattier fisher fishier freezers freesias gallon galleon gallons galleons genus genius gluer glue-ear greaser greasier groover groovier harder hardier header headier jumper jumpier laser lazier lodgers loggias lunar loonier lustre lustier manger mangier meter meatier meters meteors mirrored myriad mister mistier mitre mightier moulder moldier mugger muggier muster mustier natter nattier nipper nippier oiler oilier orals oriels pallor pallier palmer palmier Peter peatier plumber plummier plusher plushier poker pokier potter pottier psalter saltier racer racier ratter rattier reader reedier redder readier rocker rockier roomer roomier rudder ruddier runner runnier salvers salvias sapper sappier saucer saucier saver saviour savers saviours scatter scattier serous serious shaker shakier sirrah Syria sketcher sketchier sleeper sleepier smoker smokier snorter snortier sofa Sofia sponger spongier spotter spottier squeaker squeakier steamer steamier sticker stickier straggler stragglier stumper stumpier sweater sweatier taster tastier tatter tattier terror terrier terrors terriers twister twistier venal venial waiter weightier waiver wavier warier wearer whisper wispier wobbler wobblier
John Higgins, Shaftesbury, December 2009