I implemented it by subclassing QwtScaleDraw and modifying drawLabel and drawBackbone. Works quite well. The inspiration came from qtiplot, which uses the same approach. There is some gap between the non-major ticks and the grid, but I guess thats just not avoidable due to Scale and Plot being different widgets.

Here is the relevant code:
Qt Code: 
  1. void ScaleDraw::drawTick(QPainter *painter, double value, int len) const {
  2.     if (m_tickDirection == outwards)
  3.         return QwtScaleDraw::drawTick(painter, value, len);
  4.  
  5.     if ( len <= 0 )
  6.         return;
  7.  
  8.     int pw2 = qMin((int)painter->pen().width(), len) / 2;
  9.  
  10.     QwtScaleMap scaleMap = map();
  11.     const QwtMetricsMap metricsMap = QwtPainter::metricsMap();
  12.     QPoint pos = this->pos();
  13.  
  14.     if ( !metricsMap.isIdentity() )
  15.     {
  16.         /*
  17.            The perfect position of the ticks is important.
  18.            To avoid rounding errors we have to use
  19.            device coordinates.
  20.          */
  21.         QwtPainter::resetMetricsMap();
  22.  
  23.         pos = metricsMap.layoutToDevice(pos);
  24.  
  25.         if ( orientation() == Qt::Vertical )
  26.         {
  27.             scaleMap.setPaintInterval(
  28.                 metricsMap.layoutToDeviceY((int)scaleMap.p1()),
  29.                 metricsMap.layoutToDeviceY((int)scaleMap.p2())
  30.             );
  31.             len = metricsMap.layoutToDeviceX(len);
  32.         }
  33.         else
  34.         {
  35.             scaleMap.setPaintInterval(
  36.                 metricsMap.layoutToDeviceX((int)scaleMap.p1()),
  37.                 metricsMap.layoutToDeviceX((int)scaleMap.p2())
  38.             );
  39.             len = metricsMap.layoutToDeviceY(len);
  40.         }
  41.     }
  42.  
  43.     const int tval = scaleMap.transform(value);
  44.  
  45.     switch(alignment())
  46.     {
  47.         case LeftScale:
  48.         {
  49.                 QwtPainter::drawLine(painter, pos.x() - pw2 - majTickLength(), tval,
  50.                     pos.x() + len - majTickLength(), tval);
  51.  
  52.             break;
  53.         }
  54.  
  55.         case RightScale:
  56.         {
  57.                 QwtPainter::drawLine(painter, pos.x() + pw2 + majTickLength(), tval,
  58.                     pos.x() - len + majTickLength(), tval);
  59.             break;
  60.         }
  61.  
  62.         case BottomScale:
  63.         {
  64.             QwtPainter::drawLine(painter, tval, pos.y() + pw2 + majTickLength(),
  65.                 tval, pos.y() - len + majTickLength());
  66.             break;
  67.         }
  68.  
  69.         case TopScale:
  70.         {
  71.                 QwtPainter::drawLine(painter, tval, pos.y() - pw2 - majTickLength(),
  72.                     tval, pos.y() - majTickLength() + len);
  73.             break;
  74.         }
  75.     }
  76.     QwtPainter::setMetricsMap(metricsMap); // restore metrics map
  77. }
  78.  
  79. /*!
  80.    Draws the baseline of the scale
  81.    \param painter Painter
  82.  
  83.    \sa drawTick(), drawLabel()
  84. */
  85. void ScaleDraw::drawBackbone(QPainter *painter) const
  86. {
  87.     if (m_tickDirection == outwards)
  88.         return QwtScaleDraw::drawBackbone(painter);
  89.  
  90.     const int bw2 = painter->pen().width() / 2;
  91.  
  92.     const QPoint &pos = this->pos();
  93.     const int len = length() - 1;
  94.  
  95.     switch(alignment())
  96.     {
  97.         case LeftScale: {
  98.             double leftShift = majTickLength();
  99.             QwtPainter::drawLine(painter, pos.x() - bw2 - leftShift,
  100.                 pos.y(), pos.x() - bw2 - leftShift, pos.y() + len );
  101.             break;
  102.         }
  103.         case RightScale: {
  104.             double rightShift = majTickLength();
  105.             QwtPainter::drawLine(painter, pos.x() + bw2 + rightShift,
  106.                 pos.y(), pos.x() + bw2 + rightShift, pos.y() + len);
  107.             break;
  108.         }
  109.         case TopScale: {
  110.             double upShift = majTickLength();
  111.             QwtPainter::drawLine(painter, pos.x(), pos.y() - bw2 - upShift,
  112.                 pos.x() + len, pos.y() - bw2 - upShift);
  113.             break;
  114.         }
  115.         case BottomScale: {
  116.             double downShift = majTickLength();
  117.             QwtPainter::drawLine(painter, pos.x(), pos.y() + bw2 + downShift,
  118.                 pos.x() + len, pos.y() + bw2 + downShift);
  119.             break;
  120.         }
  121.     }
  122. }
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This is still based on Qwt 5.x, I'll do the upgrade soon.

So thanks for you help!